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

MEDIUM

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Is frictional force a conservative force or a non-conservative force? Why is it called so?

Important Questions on Work, Power and Energy

MEDIUM

Physics>Mechanics>Work, Power and Energy>Conservative and Non-conservative Forces

Which of the following is not a correct statement?

EASY

Physics>Mechanics>Work, Power and Energy>Conservative and Non-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, Power and Energy>Conservative and Non-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, Power and Energy>Conservative and Non-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, Power and Energy>Conservative and Non-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, Power and Energy>Conservative and Non-conservative Forces

Which one of the following is not a conservative force?

EASY

Physics>Mechanics>Work, Power and Energy>Conservative and Non-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

MEDIUM

Physics>Mechanics>Work, Power and Energy>Conservative and Non-conservative Forces

When a rubber-band is stretched by a distance x, it exerts a restoring force of magnitude
F = ax + bx² where a and b are constants. The work done in stretching the unstretched rubber-band by L is :

HARD

Physics>Mechanics>Work, Power and Energy>Conservative and Non-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

MEDIUM

Physics>Mechanics>Work, Power and Energy>Conservative and Non-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, Power and Energy>Conservative and Non-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, Power and Energy>Conservative and Non-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, Power and Energy>Conservative and Non-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

MEDIUM

Physics>Mechanics>Work, Power and Energy>Conservative and Non-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)	$\frac{d P}{d t}$

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Physics>Mechanics>Work, Power and Energy>Conservative and Non-conservative Forces

A block of mass

m

is kept on a platform which starts from rest with a constant acceleration

\frac{g}{2}

upwards, as shown in the figure. Work done by normal reaction on block in time

t

is,

MEDIUM

Physics>Mechanics>Work, Power and Energy>Conservative and Non-conservative Forces

A time dependent force

F = 6 t

acts on a particle of mass

1 kg

. If the particle starts from the rest, the work done by the force during the first

1 \sec

will be:

EASY

Physics>Mechanics>Work, Power and Energy>Conservative and Non-conservative Forces

A particle moves from a point

(- 2 \hat{i} + 5 \hat{j})

(4 \hat{j} + 3 \hat{k})

when a force of

(4 \hat{i} + 3 \hat{j}) N

is applied. How much work has been done by the force?

EASY

Physics>Mechanics>Work, Power and Energy>Conservative and Non-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, Power and Energy>Conservative and Non-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, Power and Energy>Conservative and Non-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,

Is frictional force a conservative force or a non-conservative force? Why is it called so?

Important Questions on Work, Power and Energy

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