An elastic ring of mass m and force constant k (stiffness) is released from rest in a smooth cone of semi vertex angle θ from horizontal position as shown in figure. Initially the ring was in natural length:

Maximum vertical displacement of centre of ring is m g cot 2 θ 2 π 2 k

Initial acceleration of any point on circumference of the ring is g .

Initial acceleration of centre of ring is g cos 2 ⁡ θ

At the moment of maximum vertical displacement acceleration of centre of ring is zero.

An elastic ring of mass m and force constant k (stiffness) is released from rest in a smooth cone of semi vertex angle θ from horizontal position as shown in figure. Initially the ring was in natural length:

Maximum vertical displacement of centre of ring is m g cot 2 θ 2 π 2 k

An elastic ring of mass m and force constant k stiffness is released from rest in a smooth cone of semi vertex angle from horizontal position as shown in figure Initially the ring was in natural length

HARD

Physical Sciences>Energy>Plan and conduct an investigation to provide evidence that the transfer of thermal energy when two components of different temperature are combined within a closed system results in a more uniform energy distribution among the components in the system (second law of thermodynamics).>Conservation of Energy and Energy Transfer - Energy cannot be created or destroyed, but it can be transported from one place to another and transferred between systems.Uncontrolled systems always evolve toward more stable states—that is, toward more uniform energy distribution (e.g., water flows downhill, objects hotter than their surrounding environment cool down)

An object of mass

0.5 kg

is executing simple harmonic motion. It amplitude is

5 cm

and time period (T) is

0.2 s

. What will be the potential energy of the object at an instant

t = \frac{T}{4} s

starting from mean position. Assume that the initial phase of the oscillation is zero.

MEDIUM

Physical Sciences>Energy>Plan and conduct an investigation to provide evidence that the transfer of thermal energy when two components of different temperature are combined within a closed system results in a more uniform energy distribution among the components in the system (second law of thermodynamics).>Conservation of Energy and Energy Transfer - Energy cannot be created or destroyed, but it can be transported from one place to another and transferred between systems.Uncontrolled systems always evolve toward more stable states—that is, toward more uniform energy distribution (e.g., water flows downhill, objects hotter than their surrounding environment cool down)

A particle is executing simple harmonic motion

(S H M)

of amplitude

A,

along the

x

-axis, about

x = 0 .

When its potential Energy

(P E)

equals kinetic energy

(K E),

the position of the particle will be:

EASY

Physical Sciences>Energy>Plan and conduct an investigation to provide evidence that the transfer of thermal energy when two components of different temperature are combined within a closed system results in a more uniform energy distribution among the components in the system (second law of thermodynamics).>Conservation of Energy and Energy Transfer - Energy cannot be created or destroyed, but it can be transported from one place to another and transferred between systems.Uncontrolled systems always evolve toward more stable states—that is, toward more uniform energy distribution (e.g., water flows downhill, objects hotter than their surrounding environment cool down)

For what value of displacement the kinetic energy and potential energy of a simple harmonic oscillation become equal?

MEDIUM

Physical Sciences>Energy>Plan and conduct an investigation to provide evidence that the transfer of thermal energy when two components of different temperature are combined within a closed system results in a more uniform energy distribution among the components in the system (second law of thermodynamics).>Conservation of Energy and Energy Transfer - Energy cannot be created or destroyed, but it can be transported from one place to another and transferred between systems.Uncontrolled systems always evolve toward more stable states—that is, toward more uniform energy distribution (e.g., water flows downhill, objects hotter than their surrounding environment cool down)

A body is executing simple harmonic motion with frequency

n

, the frequency of its potential energy is

MEDIUM

Physical Sciences>Energy>Plan and conduct an investigation to provide evidence that the transfer of thermal energy when two components of different temperature are combined within a closed system results in a more uniform energy distribution among the components in the system (second law of thermodynamics).>Conservation of Energy and Energy Transfer - Energy cannot be created or destroyed, but it can be transported from one place to another and transferred between systems.Uncontrolled systems always evolve toward more stable states—that is, toward more uniform energy distribution (e.g., water flows downhill, objects hotter than their surrounding environment cool down)

The maximum value attained by the tension in the string of a swinging pendulum is four times the minimum value it attains. There is no slack in the string. The angular amplitude of the pendulum is

MEDIUM

Physical Sciences>Energy>Plan and conduct an investigation to provide evidence that the transfer of thermal energy when two components of different temperature are combined within a closed system results in a more uniform energy distribution among the components in the system (second law of thermodynamics).>Conservation of Energy and Energy Transfer - Energy cannot be created or destroyed, but it can be transported from one place to another and transferred between systems.Uncontrolled systems always evolve toward more stable states—that is, toward more uniform energy distribution (e.g., water flows downhill, objects hotter than their surrounding environment cool down)

A particle starts executing simple harmonic motion

(SHM)

of amplitude

a

and total energy

E .

At any instant, its kinetic energy is

\frac{3 E}{4}

, then its displacement

y

is given by:

EASY

Physical Sciences>Energy>Plan and conduct an investigation to provide evidence that the transfer of thermal energy when two components of different temperature are combined within a closed system results in a more uniform energy distribution among the components in the system (second law of thermodynamics).>Conservation of Energy and Energy Transfer - Energy cannot be created or destroyed, but it can be transported from one place to another and transferred between systems.Uncontrolled systems always evolve toward more stable states—that is, toward more uniform energy distribution (e.g., water flows downhill, objects hotter than their surrounding environment cool down)

A body is executing S.H.M. Its potential energy is

E_{1}

and

E_{2}

at displacements

x

and

y

respectively. The potential energy at displacement

(x + y)

is

EASY

Physical Sciences>Energy>Plan and conduct an investigation to provide evidence that the transfer of thermal energy when two components of different temperature are combined within a closed system results in a more uniform energy distribution among the components in the system (second law of thermodynamics).>Conservation of Energy and Energy Transfer - Energy cannot be created or destroyed, but it can be transported from one place to another and transferred between systems.Uncontrolled systems always evolve toward more stable states—that is, toward more uniform energy distribution (e.g., water flows downhill, objects hotter than their surrounding environment cool down)

A particle executing simple harmonic motion along a straight line with an amplitude

A

, attains maximum potential energy when its displacement from mean position equals

HARD

Physical Sciences>Energy>Plan and conduct an investigation to provide evidence that the transfer of thermal energy when two components of different temperature are combined within a closed system results in a more uniform energy distribution among the components in the system (second law of thermodynamics).>Conservation of Energy and Energy Transfer - Energy cannot be created or destroyed, but it can be transported from one place to another and transferred between systems.Uncontrolled systems always evolve toward more stable states—that is, toward more uniform energy distribution (e.g., water flows downhill, objects hotter than their surrounding environment cool down)

A potential is given by

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

for

x < 0

and

V (x) = \frac{k (x - a)^{2}}{2}

for

x > 0

. The schematic variation of oscillation period

T

for a particle performing periodic motion in this potential as a function of its energy

E

is:

EASY

Physical Sciences>Energy>Plan and conduct an investigation to provide evidence that the transfer of thermal energy when two components of different temperature are combined within a closed system results in a more uniform energy distribution among the components in the system (second law of thermodynamics).>Conservation of Energy and Energy Transfer - Energy cannot be created or destroyed, but it can be transported from one place to another and transferred between systems.Uncontrolled systems always evolve toward more stable states—that is, toward more uniform energy distribution (e.g., water flows downhill, objects hotter than their surrounding environment cool down)

The physical quantity conserved in simple harmonic motion is

MEDIUM

Physical Sciences>Energy>Plan and conduct an investigation to provide evidence that the transfer of thermal energy when two components of different temperature are combined within a closed system results in a more uniform energy distribution among the components in the system (second law of thermodynamics).>Conservation of Energy and Energy Transfer - Energy cannot be created or destroyed, but it can be transported from one place to another and transferred between systems.Uncontrolled systems always evolve toward more stable states—that is, toward more uniform energy distribution (e.g., water flows downhill, objects hotter than their surrounding environment cool down)

A mass of $5 kg$ is connected to a spring. The potential energy curve of the simple harmonic motion executed by the system is shown in the figure. A simple pendulum of length $4 m$ has the same period of oscillation as the spring system. What is the value of acceleration due to gravity on the planet where these experiments are performed ?

Question Image

MEDIUM

Physical Sciences>Energy>Plan and conduct an investigation to provide evidence that the transfer of thermal energy when two components of different temperature are combined within a closed system results in a more uniform energy distribution among the components in the system (second law of thermodynamics).>Conservation of Energy and Energy Transfer - Energy cannot be created or destroyed, but it can be transported from one place to another and transferred between systems.Uncontrolled systems always evolve toward more stable states—that is, toward more uniform energy distribution (e.g., water flows downhill, objects hotter than their surrounding environment cool down)

A particle is executing simple harmonic motion with a time period

T

. At time

t = 0

, it is at its position of equilibrium. The kinetic energy - time graph of the particle will look like:

MEDIUM

Physical Sciences>Energy>Plan and conduct an investigation to provide evidence that the transfer of thermal energy when two components of different temperature are combined within a closed system results in a more uniform energy distribution among the components in the system (second law of thermodynamics).>Conservation of Energy and Energy Transfer - Energy cannot be created or destroyed, but it can be transported from one place to another and transferred between systems.Uncontrolled systems always evolve toward more stable states—that is, toward more uniform energy distribution (e.g., water flows downhill, objects hotter than their surrounding environment cool down)

A particle of mass

1 kg

is hanging from a spring of force constant

100 N m^{- 1} .

The mass is pulled slightly downward and released so that it executes free simple harmonic motion with time period

T .

The minimum time when the kinetic energy and potential energy of the system will become equal, is

\frac{T}{n} .

The value of

n

is ________.

HARD

Physical Sciences>Energy>Plan and conduct an investigation to provide evidence that the transfer of thermal energy when two components of different temperature are combined within a closed system results in a more uniform energy distribution among the components in the system (second law of thermodynamics).>Conservation of Energy and Energy Transfer - Energy cannot be created or destroyed, but it can be transported from one place to another and transferred between systems.Uncontrolled systems always evolve toward more stable states—that is, toward more uniform energy distribution (e.g., water flows downhill, objects hotter than their surrounding environment cool down)

In a simple harmonic oscillation, what fraction of total mechanical energy is in the form of kinetic energy, when the particle is midway between mean and extreme position.

MEDIUM

Physical Sciences>Energy>Plan and conduct an investigation to provide evidence that the transfer of thermal energy when two components of different temperature are combined within a closed system results in a more uniform energy distribution among the components in the system (second law of thermodynamics).>Conservation of Energy and Energy Transfer - Energy cannot be created or destroyed, but it can be transported from one place to another and transferred between systems.Uncontrolled systems always evolve toward more stable states—that is, toward more uniform energy distribution (e.g., water flows downhill, objects hotter than their surrounding environment cool down)

For a body executing S.H.M. :
(a) Potential energy is always equal to its

K . E .

(b) Average potential and kinetic energy over any given time interval are always equal.
(c) Sum of the kinetic and potential energy at any point of time is constant.
(d) Average

K . E .

in one time period is equal to average potential energy in one time period.
Choose the most appropriate option from the options given below :

HARD

Physical Sciences>Energy>Plan and conduct an investigation to provide evidence that the transfer of thermal energy when two components of different temperature are combined within a closed system results in a more uniform energy distribution among the components in the system (second law of thermodynamics).>Conservation of Energy and Energy Transfer - Energy cannot be created or destroyed, but it can be transported from one place to another and transferred between systems.Uncontrolled systems always evolve toward more stable states—that is, toward more uniform energy distribution (e.g., water flows downhill, objects hotter than their surrounding environment cool down)

The displacement of a particle in simple harmonic motion (SHM) is given by

y = \sqrt{3 π} \sin (\frac{100}{π} t + \frac{π}{4}) .

What will be the displacement of the particle from the mean position when its kinetic energy is eight times that of its potential energy?

HARD

Physical Sciences>Energy>Plan and conduct an investigation to provide evidence that the transfer of thermal energy when two components of different temperature are combined within a closed system results in a more uniform energy distribution among the components in the system (second law of thermodynamics).>Conservation of Energy and Energy Transfer - Energy cannot be created or destroyed, but it can be transported from one place to another and transferred between systems.Uncontrolled systems always evolve toward more stable states—that is, toward more uniform energy distribution (e.g., water flows downhill, objects hotter than their surrounding environment cool down)

A body of mass

1 kg

is executing simple harmonic motion (SHM). Its displacement

y

(in

cm

) at time t given by

y = [6 \sin (100 t + \frac{π}{4})] cm .

Its maximum kinetic energy is

MEDIUM

Physical Sciences>Energy>Plan and conduct an investigation to provide evidence that the transfer of thermal energy when two components of different temperature are combined within a closed system results in a more uniform energy distribution among the components in the system (second law of thermodynamics).>Conservation of Energy and Energy Transfer - Energy cannot be created or destroyed, but it can be transported from one place to another and transferred between systems.Uncontrolled systems always evolve toward more stable states—that is, toward more uniform energy distribution (e.g., water flows downhill, objects hotter than their surrounding environment cool down)

The total energy of a body executing simple harmonic motion is

E

. The kinetic energy when the displacement is

1 / 3

of the amplitude

EASY

Physical Sciences>Energy>Plan and conduct an investigation to provide evidence that the transfer of thermal energy when two components of different temperature are combined within a closed system results in a more uniform energy distribution among the components in the system (second law of thermodynamics).>Conservation of Energy and Energy Transfer - Energy cannot be created or destroyed, but it can be transported from one place to another and transferred between systems.Uncontrolled systems always evolve toward more stable states—that is, toward more uniform energy distribution (e.g., water flows downhill, objects hotter than their surrounding environment cool down)

A simple pendulum of length

L

has mass

M

and it oscillates freely with amplitude

A

. At the extreme position, its potential energy is (

g

= acceleration due to gravity)

HARD

Physical Sciences>Energy>Plan and conduct an investigation to provide evidence that the transfer of thermal energy when two components of different temperature are combined within a closed system results in a more uniform energy distribution among the components in the system (second law of thermodynamics).>Conservation of Energy and Energy Transfer - Energy cannot be created or destroyed, but it can be transported from one place to another and transferred between systems.Uncontrolled systems always evolve toward more stable states—that is, toward more uniform energy distribution (e.g., water flows downhill, objects hotter than their surrounding environment cool down)

For a simple pendulum, a graph is plotted between its kinetic energy (K.E.) and potential energy (P.E.) against its displacement d. which one of the following represents these correctly? (graphs are schematic and not drawn to scale)

An elastic ring of mass $m$ and force constant $k$ (stiffness) is released from rest in a smooth cone of semi vertex angle $θ$ from horizontal position as shown in figure. Initially the ring was in natural length:

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