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 of mass m is initially at rest at the origin. It is subjected to a force and starts moving along the x - axis. Its kinetic energy changes with time as d K d t = γ t , where γ is a positive constant of appropriate dimensions. Which of the following statements is (are) true?

The distance of the particle from the origin increases linearly with time

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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The potential energy of a particle of mass $5 kg$ , moving in the $x y$ plane, is given by $U = - 7 x + 24 y J, x$ and $y$ being in metres. Initially $($ at $t = 0)$ , the particle is at the origin and has velocity $\vec{v} = (14.4 \hat{i} + 4.2 \hat{j}) m s^{- 1}$ . Then:

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Important Questions on Work, Energy and Power

MEDIUM

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

Which of the following is not a correct statement?

EASY

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

MEDIUM

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

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>Kinetic 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

EASY

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

Which one of the following is not a conservative force?

EASY

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

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

EASY

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

A particle which is experiencing a force, given by

\vec{F} = 3 \hat{i} - 12 \hat{j}

, undergoes a displacement of

\vec{d} = 4 \hat{i}

. If the particle had a kinetic energy of

3 J

at the beginning of the displacement, what is its kinetic energy at the end of the displacement?

HARD

Physics>Mechanics>Work, Energy and Power>Kinetic 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

MEDIUM

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

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>Kinetic 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 :

EASY

Physics>Mechanics>Work, Energy and Power>Kinetic 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

EASY

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

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, Energy and Power>Kinetic and Potential Energy

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>Kinetic and Potential Energy

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 :

HARD

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

A particle of mass

m

is initially at rest at the origin. It is subjected to a force and starts moving along the x - axis. Its kinetic energy changes with time as

\frac{d K}{d t} = γ t,

where

γ

is a positive constant of appropriate dimensions. Which of the following statements is (are) true?

EASY

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

A force acts on a

2 kg

object so that its position is given as a function of time as

x = 3 t^{2} + 5 .

What is the work done by this force in first

5

seconds?

EASY

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

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>Kinetic 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)

MEDIUM

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

The potential energy of a particle of mass 5 kg, moving in the xy plane, is given by U=-7 x+24 y J, x and y being in metres. Initially (at t=0), the particle is at the origin and has velocity v→=14.4i^+4.2j^ m s-1. Then:

Important Questions on Work, Energy and Power

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The potential energy of a particle of mass $5 kg$ , moving in the $x y$ plane, is given by $U = - 7 x + 24 y J, x$ and $y$ being in metres. Initially $($ at $t = 0)$ , the particle is at the origin and has velocity $\vec{v} = (14.4 \hat{i} + 4.2 \hat{j}) m s^{- 1}$ . Then: