A particle with total mechanical energy which is small and negative is under the influence of a one dimensional potential U x = x 4 4 - x 2 2 J , where x is in meters. At time t = 0 s , it is at x = - 0 . 5 m . Then at a later time it can be found,

between x = - 1 . 0 m to x = 0 . 0 m

between x = - 1 . 0 m to x = 1 . 0 m

between x = 0 . 0 m to x = 1 . 0 m

EASY

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What are the conditions for a body to be in Static Equilibrium?

Important Questions on Work, Energy and Power

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Physics>Mechanics>Work, Energy and Power>Potential Energy

The potential energy of a particle in a central field has the form

U (r) = \frac{1}{r^{2}} - \frac{1}{r},

where

' r'

is the distance from the centre of the field. The magnitude of the maximum attractive force in Newton is

EASY

Physics>Mechanics>Work, Energy and Power>Potential Energy

A block of mass

100 g

moving at a speed of

2 m s^{- 1}

compresses a spring through a distance

2 cm

before its speed is halved. Find the spring constant of the spring

EASY

Physics>Mechanics>Work, Energy and Power>Potential Energy

Two equal masses are attached to two each of a spring of spring constant

k

. The masses are pulled out symmetrically to stretch the spring by a length

x

over is natural length. The work done by the spring on each mass is

MEDIUM

Physics>Mechanics>Work, Energy and Power>Potential Energy

A rod of weight

W

is supported by two parallel knife edges

A

and

B

and is in equilibrium in a horizontal position. The knives are at a distance

d

from each other. The centre of mass of the rod is at distance

x

from

A

. the normal reaction on

A

is:

HARD

Physics>Mechanics>Work, Energy and Power>Potential Energy

The potential energy

(U)

of a diatomic molecule is a function dependent on

r

(interatomic distance) as

U = \frac{α}{r^{10}} - \frac{β}{r^{5}} - 3

where,

α

and

β

are positive constants. The equilibrium distance between two atoms will be

{(\frac{2 α}{β})}^{\frac{1}{a}},

where

a =

______ .

MEDIUM

Physics>Mechanics>Work, Energy and Power>Potential Energy

A mass of

10 kg

is suspended vertically by a rope from the roof. When a horizontal force is applied on the rope at some point, the rope deviated at an angle of

45 °

at the roof point. If the suspended mass is at equilibrium, the magnitude of the force applied is

(g = 10 m s^{- 2})

MEDIUM

Physics>Mechanics>Work, Energy and Power>Potential Energy

A particle is released from a height

H

. At a certain height its kinetic energy is half of its potential energy with reference to the surface of the earth. Height and speed of the particle at that instant are respectively

EASY

Physics>Mechanics>Work, Energy and Power>Potential Energy

A particle moving with velocity $\vec{V}$ is acted by three forces shown by the vector triangle $P Q R$ . The velocity of the particle will
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MEDIUM

Physics>Mechanics>Work, Energy and Power>Potential Energy

Water falls from a height of

60 m

at the rate of

15 kg s^{- 1}

to operate a turbine. The losses due to frictional force are

10 %

of the input energy. How much power is generated by the turbine?

(g = 10 m s^{- 2})

HARD

Physics>Mechanics>Work, Energy and Power>Potential Energy

A particle is moving in a circle of radius

r

under the action of a force

F = α r^{2}

which is directed towards centre of the circle. Total mechanical energy (kinetic energy + potential energy) of the particle is (take potential energy

= 0

for

r = 0

HARD

Physics>Mechanics>Work, Energy and Power>Potential Energy

On heating water, bubbles being formed at the bottom of the vessel detatch and rise. Take the bubbles to be spheres of radius R and making a circular contact of radius r with the bottom of the vessel. If r << R, and the surface tension of water is T, value of r just before bubbles detatch is :
(density of water is

ρ_{w}

)

EASY

Physics>Mechanics>Work, Energy and Power>Potential Energy

Hydrogen ion and singly ionized helium atom are accelerated, from rest, through the same potential difference. The ratio of final speeds of hydrogen and helium ions is close to:

MEDIUM

Physics>Mechanics>Work, Energy and Power>Potential Energy

Two masses

m_{1} = 5 kg

and

m_{2} = 10 kg

, connected by an inextensible string over a frictionless pulley, are moving as shown in the figure. The coefficient of friction of horizontal surface is

0.15

. The minimum weight

m

that should be put on top of

m_{2}

to stop the motion is:

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EASY

Physics>Mechanics>Work, Energy and Power>Potential Energy

Potential energy as a function of

r

is given by

U = \frac{A}{r^{10}} - \frac{B}{r^{5}}

, where

r

is the interatomic distance,

A

and

B

are positive constants. The equilibrium distance between the two atoms will be :

MEDIUM

Physics>Mechanics>Work, Energy and Power>Potential Energy

A block of mass

10 k g

is in contact against the inner wall of a hollow cylindrical drum of radius

1 m

. The coefficient of friction between the block and the inner wall of the cylinder is

0.1

. The minimum angular velocity needed for the cylinder to keep the block stationary when the cylinder is vertical and rotating about its axis will be

(g = 10 m s^{- 2})

HARD

Physics>Mechanics>Work, Energy and Power>Potential Energy

60 H P

electric motor lifts an elevator having a maximum total load capacity of

2000 k g .

If the frictional force on the elevator is

4000 N,

the speed of the elevator at full load is close to :

(1 HP = 746 W, g = 10 m s^{- 2})

HARD

Physics>Mechanics>Work, Energy and Power>Potential Energy

A block of weight

100 N

is suspended by copper and steel wires of same cross-sectional area

0.5 c m^{2}

and, length

\sqrt{3} m

and

1 m,

respectively. Their other ends are fixed on a ceiling as shown in figure. The angles subtended by copper and steel wires with ceiling are

30^{o}

and

60^{o},

respectively. If elongation in copper wire is

(Δ l_{C})

and elongation in steel wire is

(Δ l_{S}),

then the ratio

\frac{Δ l_{C}}{Δ l_{S}}

\frac{x}{1}

.Find the value of

x

.
[Young's modulus for copper and steel are

1 \times 10^{11} N m^{- 2}

and

2 \times 10^{11} {Nm}^{- 2}

respectively]

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MEDIUM

Physics>Mechanics>Work, Energy and Power>Potential Energy

A particle with total mechanical energy which is small and negative is under the influence of a one dimensional potential

U (x) = \frac{x^{4}}{4} - \frac{x^{2}}{2} J

, where

x

is in meters. At time

t = 0 s

, it is at

x = - 0.5 m

. Then at a later time it can be found,

MEDIUM

Physics>Mechanics>Work, Energy and Power>Potential Energy

If the potential energy between two molecules is given by

U = \frac{A}{r^{6}} - \frac{B}{r^{12}},

then at equilibrium, separation between molecules, and the potential energy are:

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Physics>Mechanics>Work, Energy and Power>Potential Energy

A person trying to lose weight by burning fat lifts a mass of 10 kg upto a height of 1m 1000 times. Assume that the potential energy lost each time he lowers the mass is dissipated. How much fat will he use up considering the work done only when the weight is lifted up? Fat supplies

3.8 \times 10^{7}

J of energy per kg which is converted to mechanical energy with a 20% efficiency rate. Take

g = 9.8 m s^{- 2}

What are the conditions for a body to be in Static Equilibrium?

Important Questions on Work, Energy and Power

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