Match the following? Column-I Column-II (a) F net (i) d K d t (b) F cons (ii) Δ U + Δ K (c) ∑ W non-cons (iii) - d U d x (d) Power (iv) d P d t

(a-iii), (b-ii), (c-ii), (d-ii)

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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A particle is released from rest at origin. It moves under the influence of potential field $U = x^{2} - 3 x$ .
Its kinetic energy at $x = 2$ is

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Important Questions on Work, Energy and Power

MEDIUM

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

Which of the following is not a correct statement?

EASY

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

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>Potential Energy and Conservative Forces

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

MEDIUM

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

A particle of mass

m

moves under the influence of the potential

V (x) = P / x^{2} - Q / x

. Here

P, Q

are real positive constants. The angular frequency of small oscillations of the particle around the equilibrium point is

MEDIUM

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

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 and Conservative Forces

Which one of the following is not a conservative force?

EASY

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

The potential energy of a particle varies with distance

' x'

as shown in the graph. The force acting on the particle is zero at
Question Image

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

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

HARD

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

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

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

The graphs below show the magnitude of the force on a particle as it moves along the positive $X$ -axis from the origin to $X = X_{1}$ . The force is parallel to the $X$ -axis and conservative. The maximum magnitude $F_{1}$ has the same value for all graphs. Rank the situations according to the change in the potential energy associated with the force, least (or most negative) to greatest (or most positive).

Question Image

EASY

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

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 :

EASY

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

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 and Conservative Forces

The potential energy of an object is

U (x) = (5 x^{2} - 4 x^{3}) J

, where

x

is the position in meter. The position at which the force becomes zero is

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

Match the following?

Column-I		Column-II
(a)	$F_{net}$	(i)	$\frac{d K}{d t}$
(b)	$F_{cons}$	(ii)	$Δ U + Δ K$
(c)	$\sum W_{non-cons}$	(iii)	$\frac{- d U}{d x}$
(d)	$Power$	(iv)	$\frac{d P}{d t}$

EASY

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

A rod of length

l

and mass

m

fixed at one end, is hanging vertically. The other end is now raised so that the rod makes an angle

30 °

with horizontal line. The work done in the process will be :

EASY

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

The figure shows the variation of potential energy with distance. The part of the graph which represents the repulsive force is

Question Image

EASY

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

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>Potential Energy and Conservative Forces

A particle of mass

m

moves in a circular orbit under the central potential field,

U (r) = \frac{- C}{r}

, where

C

is a positive constant. The correct radius - velocity graph of the particle's motion is :

MEDIUM

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

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)

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

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,

A particle is released from rest at origin. It moves under the influence of potential field U=x2-3x. Its kinetic energy at x=2 is

Important Questions on Work, Energy and Power

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A particle is released from rest at origin. It moves under the influence of potential field $U = x^{2} - 3 x$ .
Its kinetic energy at $x = 2$ is