Match List ‐ I (Event) with List ‐ II (Order of the time interval for the happening of the event) and select the correct option from the options given below the lists. List-I List-II ( a ) The rotation period of earth ( i ) 10 5 s ( b ) Revolution period of earth ( ii ) 10 7 s ( c ) Period of a light wave ( iii ) 10 - 15 s ( d ) Period of a sound wave ( iv ) 10 - 3 s

( a ) ‐ ( i ) , ( b ) ‐ ( ii ) , ( c ) ‐ ( iii ) , ( d ) ‐ ( iv )

( a ) ‐ ( ii ) , ( b ) ‐ ( i ) , ( c ) ‐ ( iii ) , ( d ) ‐ ( iv )

( a ) ‐ ( i ) , ( b ) ‐ ( ii ) , ( c ) ‐ ( iv ) , ( d ) ‐ ( iii )

( a ) ‐ ( ii ) , ( b ) ‐ ( i ) , ( c ) ‐ ( iv ) , d ‐ ( iii )

A simple pendulum of lengthl30cm and m2kg is attached to a cart of mass3kg The cart can move frictionlessly on level ground The bob is released from rest when string makes an angle of 18 with the horizontal

HARD

Physical Sciences>Energy>Develop and use models to illustrate that energy at the macroscopic scale can be accounted for as a combination of energy associated with the motions of particles (objects) and energy associated with the relative position of particles (objects).>Definitions of Energy - Energy is a quantitative property of a system that depends on the motion and interactions of matter and radiation within that system. That there is a single quantity called energy is due to the fact that a system’s total energy is conserved, even as,within the system, energy is continually transferred from one object to another and between its various possible forms.At the macroscopic scale, energy manifests itself in multiple ways, such as in motion, sound, light, and thermal energy These relationships are better understood at the microscopic scale, at which all of the different manifestations of energy can be modeled as a combination of energy associated with the motion of particles and energy associated with the configuration(relative position of the particles). In some cases the relative position energy can be thought of as stored in fields (which mediate interactions between particles). This last concept includes radiation, a phenomenon in which energy stored in fields moves across space.The availability of energy limits what can occur in any system.

A particle executes simple harmonic motion and it is located at

x = a, b

and

c

at time

t_{0}, 2 t_{0} a n d 3 t_{0}

respectively. The frequency of the oscillation is:

EASY

Physical Sciences>Energy>Develop and use models to illustrate that energy at the macroscopic scale can be accounted for as a combination of energy associated with the motions of particles (objects) and energy associated with the relative position of particles (objects).>Definitions of Energy - Energy is a quantitative property of a system that depends on the motion and interactions of matter and radiation within that system. That there is a single quantity called energy is due to the fact that a system’s total energy is conserved, even as,within the system, energy is continually transferred from one object to another and between its various possible forms.At the macroscopic scale, energy manifests itself in multiple ways, such as in motion, sound, light, and thermal energy These relationships are better understood at the microscopic scale, at which all of the different manifestations of energy can be modeled as a combination of energy associated with the motion of particles and energy associated with the configuration(relative position of the particles). In some cases the relative position energy can be thought of as stored in fields (which mediate interactions between particles). This last concept includes radiation, a phenomenon in which energy stored in fields moves across space.The availability of energy limits what can occur in any system.

A mass

M

is suspended from a spring of negligible mass. The spring is pulled a little and then released so that the mass executes

S . H . M .

of period

T

. If the mass is increased by

m

, the time period becomes

\frac{5 T}{3} .

What is the ratio

(\frac{M}{m})

?

EASY

Physical Sciences>Energy>Develop and use models to illustrate that energy at the macroscopic scale can be accounted for as a combination of energy associated with the motions of particles (objects) and energy associated with the relative position of particles (objects).>Definitions of Energy - Energy is a quantitative property of a system that depends on the motion and interactions of matter and radiation within that system. That there is a single quantity called energy is due to the fact that a system’s total energy is conserved, even as,within the system, energy is continually transferred from one object to another and between its various possible forms.At the macroscopic scale, energy manifests itself in multiple ways, such as in motion, sound, light, and thermal energy These relationships are better understood at the microscopic scale, at which all of the different manifestations of energy can be modeled as a combination of energy associated with the motion of particles and energy associated with the configuration(relative position of the particles). In some cases the relative position energy can be thought of as stored in fields (which mediate interactions between particles). This last concept includes radiation, a phenomenon in which energy stored in fields moves across space.The availability of energy limits what can occur in any system.

Assume that a tunnel is dug along a chord of the earth, at a perpendicular distance

\frac{R}{2}

from the earth's centre, where

R

is the radius of the earth. The wall of the tunnel is frictionless. If a particle is released in this tunnel, it will execute a simple harmonic motion with a time period:

EASY

Physical Sciences>Energy>Develop and use models to illustrate that energy at the macroscopic scale can be accounted for as a combination of energy associated with the motions of particles (objects) and energy associated with the relative position of particles (objects).>Definitions of Energy - Energy is a quantitative property of a system that depends on the motion and interactions of matter and radiation within that system. That there is a single quantity called energy is due to the fact that a system’s total energy is conserved, even as,within the system, energy is continually transferred from one object to another and between its various possible forms.At the macroscopic scale, energy manifests itself in multiple ways, such as in motion, sound, light, and thermal energy These relationships are better understood at the microscopic scale, at which all of the different manifestations of energy can be modeled as a combination of energy associated with the motion of particles and energy associated with the configuration(relative position of the particles). In some cases the relative position energy can be thought of as stored in fields (which mediate interactions between particles). This last concept includes radiation, a phenomenon in which energy stored in fields moves across space.The availability of energy limits what can occur in any system.

The function of time representing a simple harmonic motion with a period of

\frac{π}{ω}

is :

EASY

Physical Sciences>Energy>Develop and use models to illustrate that energy at the macroscopic scale can be accounted for as a combination of energy associated with the motions of particles (objects) and energy associated with the relative position of particles (objects).>Definitions of Energy - Energy is a quantitative property of a system that depends on the motion and interactions of matter and radiation within that system. That there is a single quantity called energy is due to the fact that a system’s total energy is conserved, even as,within the system, energy is continually transferred from one object to another and between its various possible forms.At the macroscopic scale, energy manifests itself in multiple ways, such as in motion, sound, light, and thermal energy These relationships are better understood at the microscopic scale, at which all of the different manifestations of energy can be modeled as a combination of energy associated with the motion of particles and energy associated with the configuration(relative position of the particles). In some cases the relative position energy can be thought of as stored in fields (which mediate interactions between particles). This last concept includes radiation, a phenomenon in which energy stored in fields moves across space.The availability of energy limits what can occur in any system.

A particle of mass

m

is moving along the

x - a x i s

under the potential

V (x) = \frac{k x^{2}}{2} + \frac{λ}{x^{'}}

where

k

and

x^{'}

are positive constants of appropriate dimensions. The particle is slightly displaced from its equilibrium position. The particle oscillates with the angular frequency

(ω)

given by

EASY

Physical Sciences>Energy>Develop and use models to illustrate that energy at the macroscopic scale can be accounted for as a combination of energy associated with the motions of particles (objects) and energy associated with the relative position of particles (objects).>Definitions of Energy - Energy is a quantitative property of a system that depends on the motion and interactions of matter and radiation within that system. That there is a single quantity called energy is due to the fact that a system’s total energy is conserved, even as,within the system, energy is continually transferred from one object to another and between its various possible forms.At the macroscopic scale, energy manifests itself in multiple ways, such as in motion, sound, light, and thermal energy These relationships are better understood at the microscopic scale, at which all of the different manifestations of energy can be modeled as a combination of energy associated with the motion of particles and energy associated with the configuration(relative position of the particles). In some cases the relative position energy can be thought of as stored in fields (which mediate interactions between particles). This last concept includes radiation, a phenomenon in which energy stored in fields moves across space.The availability of energy limits what can occur in any system.

A particle performs simple harmonic motion with a period of

2

second. The time taken by the particle to cover a displacement equal to half of its amplitude from the mean position is

\frac{1}{a} s .

The value of

a

to the nearest integer is

MEDIUM

Physical Sciences>Energy>Develop and use models to illustrate that energy at the macroscopic scale can be accounted for as a combination of energy associated with the motions of particles (objects) and energy associated with the relative position of particles (objects).>Definitions of Energy - Energy is a quantitative property of a system that depends on the motion and interactions of matter and radiation within that system. That there is a single quantity called energy is due to the fact that a system’s total energy is conserved, even as,within the system, energy is continually transferred from one object to another and between its various possible forms.At the macroscopic scale, energy manifests itself in multiple ways, such as in motion, sound, light, and thermal energy These relationships are better understood at the microscopic scale, at which all of the different manifestations of energy can be modeled as a combination of energy associated with the motion of particles and energy associated with the configuration(relative position of the particles). In some cases the relative position energy can be thought of as stored in fields (which mediate interactions between particles). This last concept includes radiation, a phenomenon in which energy stored in fields moves across space.The availability of energy limits what can occur in any system.

An object was found to make oscillations governed by the equation

y = \cos^{2} (ω t + \frac{π}{4}) - 0.5

. The amplitude and angular frequency of these oscillations, respectively, are

MEDIUM

Physical Sciences>Energy>Develop and use models to illustrate that energy at the macroscopic scale can be accounted for as a combination of energy associated with the motions of particles (objects) and energy associated with the relative position of particles (objects).>Definitions of Energy - Energy is a quantitative property of a system that depends on the motion and interactions of matter and radiation within that system. That there is a single quantity called energy is due to the fact that a system’s total energy is conserved, even as,within the system, energy is continually transferred from one object to another and between its various possible forms.At the macroscopic scale, energy manifests itself in multiple ways, such as in motion, sound, light, and thermal energy These relationships are better understood at the microscopic scale, at which all of the different manifestations of energy can be modeled as a combination of energy associated with the motion of particles and energy associated with the configuration(relative position of the particles). In some cases the relative position energy can be thought of as stored in fields (which mediate interactions between particles). This last concept includes radiation, a phenomenon in which energy stored in fields moves across space.The availability of energy limits what can occur in any system.

A body of mass

1 kg

is made to oscillate on a spring of force constant

15 N / m

. Calculate the angular frequency

MEDIUM

Physical Sciences>Energy>Develop and use models to illustrate that energy at the macroscopic scale can be accounted for as a combination of energy associated with the motions of particles (objects) and energy associated with the relative position of particles (objects).>Definitions of Energy - Energy is a quantitative property of a system that depends on the motion and interactions of matter and radiation within that system. That there is a single quantity called energy is due to the fact that a system’s total energy is conserved, even as,within the system, energy is continually transferred from one object to another and between its various possible forms.At the macroscopic scale, energy manifests itself in multiple ways, such as in motion, sound, light, and thermal energy These relationships are better understood at the microscopic scale, at which all of the different manifestations of energy can be modeled as a combination of energy associated with the motion of particles and energy associated with the configuration(relative position of the particles). In some cases the relative position energy can be thought of as stored in fields (which mediate interactions between particles). This last concept includes radiation, a phenomenon in which energy stored in fields moves across space.The availability of energy limits what can occur in any system.

A simple harmonic oscillator of frequency

1 Hz

has a phase of

1

radian. By how much should the origin be shifted in time so as to make the phase of the oscillator vanish. (time in seconds).

MEDIUM

Physical Sciences>Energy>Develop and use models to illustrate that energy at the macroscopic scale can be accounted for as a combination of energy associated with the motions of particles (objects) and energy associated with the relative position of particles (objects).>Definitions of Energy - Energy is a quantitative property of a system that depends on the motion and interactions of matter and radiation within that system. That there is a single quantity called energy is due to the fact that a system’s total energy is conserved, even as,within the system, energy is continually transferred from one object to another and between its various possible forms.At the macroscopic scale, energy manifests itself in multiple ways, such as in motion, sound, light, and thermal energy These relationships are better understood at the microscopic scale, at which all of the different manifestations of energy can be modeled as a combination of energy associated with the motion of particles and energy associated with the configuration(relative position of the particles). In some cases the relative position energy can be thought of as stored in fields (which mediate interactions between particles). This last concept includes radiation, a phenomenon in which energy stored in fields moves across space.The availability of energy limits what can occur in any system.

The function

(\sin ω t - \cos ω t)

represents the S.H.M having a time period

T

MEDIUM

Physical Sciences>Energy>Develop and use models to illustrate that energy at the macroscopic scale can be accounted for as a combination of energy associated with the motions of particles (objects) and energy associated with the relative position of particles (objects).>Definitions of Energy - Energy is a quantitative property of a system that depends on the motion and interactions of matter and radiation within that system. That there is a single quantity called energy is due to the fact that a system’s total energy is conserved, even as,within the system, energy is continually transferred from one object to another and between its various possible forms.At the macroscopic scale, energy manifests itself in multiple ways, such as in motion, sound, light, and thermal energy These relationships are better understood at the microscopic scale, at which all of the different manifestations of energy can be modeled as a combination of energy associated with the motion of particles and energy associated with the configuration(relative position of the particles). In some cases the relative position energy can be thought of as stored in fields (which mediate interactions between particles). This last concept includes radiation, a phenomenon in which energy stored in fields moves across space.The availability of energy limits what can occur in any system.

A simple pendulum suspended from the ceiling of a stationary lift has a time period $T_{0}$ . When the lift descends at uniform speed, the time period is $T_{1}$ . When the lift descends with constant acceleration, the time period is $T_{2}$ . Which of the following is correct?

HARD

Physical Sciences>Energy>Develop and use models to illustrate that energy at the macroscopic scale can be accounted for as a combination of energy associated with the motions of particles (objects) and energy associated with the relative position of particles (objects).>Definitions of Energy - Energy is a quantitative property of a system that depends on the motion and interactions of matter and radiation within that system. That there is a single quantity called energy is due to the fact that a system’s total energy is conserved, even as,within the system, energy is continually transferred from one object to another and between its various possible forms.At the macroscopic scale, energy manifests itself in multiple ways, such as in motion, sound, light, and thermal energy These relationships are better understood at the microscopic scale, at which all of the different manifestations of energy can be modeled as a combination of energy associated with the motion of particles and energy associated with the configuration(relative position of the particles). In some cases the relative position energy can be thought of as stored in fields (which mediate interactions between particles). This last concept includes radiation, a phenomenon in which energy stored in fields moves across space.The availability of energy limits what can occur in any system.

A load of mass $m$ falls from a height $h$ on the scale pan hung from a spring as shown. If the spring constant is $k$ and the mass of the scale pan is zero and the mass $m$ does not bounce relative to the pan, then the amplitude of vibration is

Question Image

MEDIUM

Physical Sciences>Energy>Develop and use models to illustrate that energy at the macroscopic scale can be accounted for as a combination of energy associated with the motions of particles (objects) and energy associated with the relative position of particles (objects).>Definitions of Energy - Energy is a quantitative property of a system that depends on the motion and interactions of matter and radiation within that system. That there is a single quantity called energy is due to the fact that a system’s total energy is conserved, even as,within the system, energy is continually transferred from one object to another and between its various possible forms.At the macroscopic scale, energy manifests itself in multiple ways, such as in motion, sound, light, and thermal energy These relationships are better understood at the microscopic scale, at which all of the different manifestations of energy can be modeled as a combination of energy associated with the motion of particles and energy associated with the configuration(relative position of the particles). In some cases the relative position energy can be thought of as stored in fields (which mediate interactions between particles). This last concept includes radiation, a phenomenon in which energy stored in fields moves across space.The availability of energy limits what can occur in any system.

A wave along a string has the following equation

y = 0.05 \sin (28 t - 1.78 x) m

(where,

t

is in seconds and

x

is in meters). What are the amplitude

(A),

frequency

(f)

and wavelength

(λ)

of the wave ?

HARD

Physical Sciences>Energy>Develop and use models to illustrate that energy at the macroscopic scale can be accounted for as a combination of energy associated with the motions of particles (objects) and energy associated with the relative position of particles (objects).>Definitions of Energy - Energy is a quantitative property of a system that depends on the motion and interactions of matter and radiation within that system. That there is a single quantity called energy is due to the fact that a system’s total energy is conserved, even as,within the system, energy is continually transferred from one object to another and between its various possible forms.At the macroscopic scale, energy manifests itself in multiple ways, such as in motion, sound, light, and thermal energy These relationships are better understood at the microscopic scale, at which all of the different manifestations of energy can be modeled as a combination of energy associated with the motion of particles and energy associated with the configuration(relative position of the particles). In some cases the relative position energy can be thought of as stored in fields (which mediate interactions between particles). This last concept includes radiation, a phenomenon in which energy stored in fields moves across space.The availability of energy limits what can occur in any system.

An ideal gas enclosed in a vertical cylindrical container supports a freely moving piston of mass $M$ . The piston and the cylinder have equal cross-sectional area $A$ . When the piston is in equilibrium, the volume of the gas is $V_{0}$ and its pressure is $M_{0}$ . The piston is slightly displaced from the equilibrium position and released. Assuming that the system is completely isolated from its surrounding, the piston executes a simple harmonic motion with frequency
[Assume the system is in space.]

MEDIUM

Physical Sciences>Energy>Develop and use models to illustrate that energy at the macroscopic scale can be accounted for as a combination of energy associated with the motions of particles (objects) and energy associated with the relative position of particles (objects).>Definitions of Energy - Energy is a quantitative property of a system that depends on the motion and interactions of matter and radiation within that system. That there is a single quantity called energy is due to the fact that a system’s total energy is conserved, even as,within the system, energy is continually transferred from one object to another and between its various possible forms.At the macroscopic scale, energy manifests itself in multiple ways, such as in motion, sound, light, and thermal energy These relationships are better understood at the microscopic scale, at which all of the different manifestations of energy can be modeled as a combination of energy associated with the motion of particles and energy associated with the configuration(relative position of the particles). In some cases the relative position energy can be thought of as stored in fields (which mediate interactions between particles). This last concept includes radiation, a phenomenon in which energy stored in fields moves across space.The availability of energy limits what can occur in any system.

A body of mass

1 kg

is made to oscillate on a spring of force constant

15 N / m

. Calculate the frequency of vibrations.

EASY

Physical Sciences>Energy>Develop and use models to illustrate that energy at the macroscopic scale can be accounted for as a combination of energy associated with the motions of particles (objects) and energy associated with the relative position of particles (objects).>Definitions of Energy - Energy is a quantitative property of a system that depends on the motion and interactions of matter and radiation within that system. That there is a single quantity called energy is due to the fact that a system’s total energy is conserved, even as,within the system, energy is continually transferred from one object to another and between its various possible forms.At the macroscopic scale, energy manifests itself in multiple ways, such as in motion, sound, light, and thermal energy These relationships are better understood at the microscopic scale, at which all of the different manifestations of energy can be modeled as a combination of energy associated with the motion of particles and energy associated with the configuration(relative position of the particles). In some cases the relative position energy can be thought of as stored in fields (which mediate interactions between particles). This last concept includes radiation, a phenomenon in which energy stored in fields moves across space.The availability of energy limits what can occur in any system.

The displacement of simple harmonic oscillator after

3

seconds starting from its mean position is equal to half of its amplitude. The time period of harmonic motion is

EASY

Physical Sciences>Energy>Develop and use models to illustrate that energy at the macroscopic scale can be accounted for as a combination of energy associated with the motions of particles (objects) and energy associated with the relative position of particles (objects).>Definitions of Energy - Energy is a quantitative property of a system that depends on the motion and interactions of matter and radiation within that system. That there is a single quantity called energy is due to the fact that a system’s total energy is conserved, even as,within the system, energy is continually transferred from one object to another and between its various possible forms.At the macroscopic scale, energy manifests itself in multiple ways, such as in motion, sound, light, and thermal energy These relationships are better understood at the microscopic scale, at which all of the different manifestations of energy can be modeled as a combination of energy associated with the motion of particles and energy associated with the configuration(relative position of the particles). In some cases the relative position energy can be thought of as stored in fields (which mediate interactions between particles). This last concept includes radiation, a phenomenon in which energy stored in fields moves across space.The availability of energy limits what can occur in any system.

Two massless springs with spring constants

2 k

and

9 k

, carry

50 g

and

100 g

masses at their free ends. These two masses oscillate vertically such that their maximum velocities are equal. Then, the ratio of their respective amplitudes will be :

EASY

Physical Sciences>Energy>Develop and use models to illustrate that energy at the macroscopic scale can be accounted for as a combination of energy associated with the motions of particles (objects) and energy associated with the relative position of particles (objects).>Definitions of Energy - Energy is a quantitative property of a system that depends on the motion and interactions of matter and radiation within that system. That there is a single quantity called energy is due to the fact that a system’s total energy is conserved, even as,within the system, energy is continually transferred from one object to another and between its various possible forms.At the macroscopic scale, energy manifests itself in multiple ways, such as in motion, sound, light, and thermal energy These relationships are better understood at the microscopic scale, at which all of the different manifestations of energy can be modeled as a combination of energy associated with the motion of particles and energy associated with the configuration(relative position of the particles). In some cases the relative position energy can be thought of as stored in fields (which mediate interactions between particles). This last concept includes radiation, a phenomenon in which energy stored in fields moves across space.The availability of energy limits what can occur in any system.

The weight suspended from a spring oscillates up and down. The acceleration of weight will be zero at

MEDIUM

Physical Sciences>Energy>Develop and use models to illustrate that energy at the macroscopic scale can be accounted for as a combination of energy associated with the motions of particles (objects) and energy associated with the relative position of particles (objects).>Definitions of Energy - Energy is a quantitative property of a system that depends on the motion and interactions of matter and radiation within that system. That there is a single quantity called energy is due to the fact that a system’s total energy is conserved, even as,within the system, energy is continually transferred from one object to another and between its various possible forms.At the macroscopic scale, energy manifests itself in multiple ways, such as in motion, sound, light, and thermal energy These relationships are better understood at the microscopic scale, at which all of the different manifestations of energy can be modeled as a combination of energy associated with the motion of particles and energy associated with the configuration(relative position of the particles). In some cases the relative position energy can be thought of as stored in fields (which mediate interactions between particles). This last concept includes radiation, a phenomenon in which energy stored in fields moves across space.The availability of energy limits what can occur in any system.

Frequency of oscillation of a body is

5 Hz

when a force

F_{1}

is applied and

12 Hz

when another force

F_{2}

is applied. If both forces

F_{1}

and

F_{2}

are applied together, then frequency of oscillation of the body will be

HARD

Physical Sciences>Energy>Develop and use models to illustrate that energy at the macroscopic scale can be accounted for as a combination of energy associated with the motions of particles (objects) and energy associated with the relative position of particles (objects).>Definitions of Energy - Energy is a quantitative property of a system that depends on the motion and interactions of matter and radiation within that system. That there is a single quantity called energy is due to the fact that a system’s total energy is conserved, even as,within the system, energy is continually transferred from one object to another and between its various possible forms.At the macroscopic scale, energy manifests itself in multiple ways, such as in motion, sound, light, and thermal energy These relationships are better understood at the microscopic scale, at which all of the different manifestations of energy can be modeled as a combination of energy associated with the motion of particles and energy associated with the configuration(relative position of the particles). In some cases the relative position energy can be thought of as stored in fields (which mediate interactions between particles). This last concept includes radiation, a phenomenon in which energy stored in fields moves across space.The availability of energy limits what can occur in any system.

Match List $‐ I$ (Event) with List $‐ II$ (Order of the time interval for the happening of the event) and select the correct option from the options given below the lists.

	List-I		List-II
$(a)$	The rotation period of earth	$(i)$	$10^{5} s$
$(b)$	Revolution period of earth	$(ii)$	$10^{7} s$
$(c)$	Period of a light wave	$(iii)$	$10^{- 15} s$
$(d)$	Period of a sound wave	$(iv)$	$10^{- 3} s$

A simple pendulum of length, $l = 30 cm$ and $m = 2 kg$ is attached to a cart of mass, $3 kg$ . The cart can move frictionlessly on level ground. The bob is released from rest when string makes an angle of $1.8 °$ with the horizontal:-

Important Questions on Develop and use models to illustrate that energy at the macroscopic scale can be accounted for as a combination of energy associated with the motions of particles (objects) and energy associated with the relative position of particles (objects).

Learn and Prepare for any exam you want !

A simple pendulum of length, l=30 cm and m=2 kg is attached to a cart of mass, 3 kg . The cart can move frictionlessly on level ground. The bob is released from rest when string makes an angle of 1.8° with the horizontal:-

Important Questions on Develop and use models to illustrate that energy at the macroscopic scale can be accounted for as a combination of energy associated with the motions of particles (objects) and energy associated with the relative position of particles (objects).

Learn and Prepare for any exam you want !

A simple pendulum of length, $l = 30 cm$ and $m = 2 kg$ is attached to a cart of mass, $3 kg$ . The cart can move frictionlessly on level ground. The bob is released from rest when string makes an angle of $1.8 °$ with the horizontal:-