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

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An object placed on the ground is in stable equilibrium. If the object is given a slight push, then initially the position of centre of gravity

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Important Questions on Work, Energy and Power

EASY

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

Two particles

A

and

B

of same mass have their de-Broglie wavelengths in the ratio

X_{A} : X_{B} = K : 1 .

Their potential energies

U_{A} : U_{B} = 1 : K^{2} .

The ratio of their total energies

E_{A} : E_{B}

EASY

Physics>Mechanics>Work, Energy and Power>Conservative Force and 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

HARD

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

Consider two masses with

m_{1} > m_{2}

connected by a light inextensible string that passes over a pulley of radius

R

and moment of inertia

I

about its axis of rotation. The string does not slip on the pulley and the pulley turns without friction. The two masses are released from rest separated by a vertical distance

2 h .

When the two masses pass each other, the speed of the masses is proportional to

EASY

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

Blocks of masses

m, 2 m, 4 m

and

8 m

are arranged in a line of a frictionless floor. Another block of mass

m

, moving with speed

υ

along the same line (see figure) collides with mass

m

in perfectly inelastic manner. All the subsequent collisions are also perfectly inelastic. By the time the last block of mass

8 m

starts moving the total energy loss is

p %

of the original energy. Value of

p

is close to:
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HARD

Physics>Mechanics>Work, Energy and Power>Conservative Force and 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

EASY

Physics>Mechanics>Work, Energy and Power>Conservative Force and 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:

EASY

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

A uniform chain of mass

M

and length

L

is lying on a smooth horizontal table, with half of its length hanging down. The work done in pulling the entire chain up the table is

MEDIUM

Physics>Mechanics>Work, Energy and Power>Conservative Force and 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

HARD

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

A mass of $0.5 kg$ moving with a speed of $1.5 m s^{- 1}$ on a horizontal smooth surface, collides with a nearly weightless spring of force constant $k = 50 N m^{- 1}$ . The maximum compression of the spring would be

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MEDIUM

Physics>Mechanics>Work, Energy and Power>Conservative Force and 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:

MEDIUM

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

An asteroid of mass

m

is approaching earth, initially at a distance

10 R_{e}

with speed

v_{i} .

It hits Earth with a speed

v_{f},

(R_{e}

and

M_{e}

are radius and mass of earth

)

, then

MEDIUM

Physics>Mechanics>Work, Energy and Power>Conservative Force and 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}

MEDIUM

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

A body is moving unidirectionally under the influence of a source of constant power. The square of its displacement in time

t

is proportional to

MEDIUM

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

The potential energy function for a two dimensional force is given by

U = 3 x^{3} y - 7 x

. The force that acts at the point

(x, y)

is (Take

\hat{i}

and

\hat{j}

as unit vectors along

X

- and

Y

- axes)

EASY

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

If a spring of spring constant

200 N m^{- 1}

is compressed by

5 cm

, then the energy stored in the spring is

EASY

Physics>Mechanics>Work, Energy and Power>Conservative Force and 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

EASY

Physics>Mechanics>Work, Energy and Power>Conservative Force and 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

MEDIUM

Physics>Mechanics>Work, Energy and Power>Conservative Force and 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,

An object placed on the ground is in stable equilibrium. If the object is given a slight push, then initially the position of centre of gravity

Important Questions on Work, Energy and Power

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