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

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What is the work to be done to increase the velocity of a car from $36 {kmh}^{- 1}$ to $72 {kmh}^{- 1}$ if the mass of the car is $1500 kg$ ?

Important Questions on Work and Energy

HARD

A particle moves in one dimension from rest under the influence of a force that varies with the distance traveled by the particle as shown in the figure. The kinetic energy of the particle after it has traveled

3 m

is:

EASY

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Some of the following equations are kinematical equations, where the symbols have their usual meaning. The

w o r k - e n e r g y

theorem is represented by

EASY

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The velocity-time graph of a particle of mass

10 kg

is shown in the figure. The net work done on the particle in the first two seconds of the motion is

Question Image

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A person of mass

M

is sitting on a swing of length

L

and swinging with an angular amplitude

θ_{0} .

If the person stands up when the swing passes through its lowest point, the work done by him, assuming that his centre of mass moves by a distance

l (l ≪ L),

is close to:

HARD

Science>Physics>Work and Energy>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

Science>Physics>Work and Energy>Energy

A bullet of mass

20 g

has an initial speed of

1 m s^{- 1}

, just before it starts penetrating a mud wall of thickness

20 c m

. If the wall offers a mean resistance of

2.5 \times 10^{- 2} N,

the speed of the bullet after emerging from the other side of the wall is close to:

EASY

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A body of mass

m = 1 kg

is moving in a medium and experiences a frictional force

F = - k v

, where

v

is the speed of the body. The initial speed is

v_{0} = 10 m s^{- 1}

and after

10

s, its energy becomes half of the initial energy. Then, the value of

k

EASY

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A cricket ball of mass

0.15 kg

is thrown vertically up by a bowling machine so that it rises to a maximum height of

20 m

after leaving the machine. If the part pushing the ball applies a constant force

F

on the ball and moves horizontally a distance of

0.2 m

while launching the ball, the value of

F (in N)

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

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A block of mass

10 kg

, moving in

x

direction with a constant speed of

10 m s^{- 1}

, is subjected to a retarding force

F = [(0 .1) x] J m^{- 1}

during its travel from

x = 20 m

30 m

. Its final kinetic energy will be:

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A body of mass

m

starts moving from rest along

x -

axis so that its velocity varies as

v = a \sqrt{s}

where

a

is a constant and

s

is the distance covered by the body. The total work done by all the forces acting on the body in the first

t

second after the start of the motion is

EASY

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A force increases the speed of body of mass

1.0 k g

from

4 m / s

8 m / s

. The work done by force is _____.

EASY

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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?

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A running boy has the same kinetic energy as that of a man of twice his mass. If the speed of the boy is

14.14 {ms}^{- 1},

the speed of the man is

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A thin and uniform rod of mass

M

and length

L

is held vertical on a floor with large friction. The rod is released from rest so that it falls by rotating about its contact-point with the floor without slipping. Which of the following statement(s) is/are correct, when the rod makes an angle

60^{o}

with vertical?
[

g

is the acceleration due to gravity]

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The Work - Energy theorem
(A)
(B)
(C)
(D)

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A small ball of mass

m

is thrown upward with velocity

u

from the ground. The ball experiences a resistive force

m k v^{2}

where

v

is its speed. The maximum height attained by the ball is :

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A particle of charge

q

and mass

m

is subjected to an electric field

E = E_{0} (1 - a x^{2})

in the

x -

direction, where

a

and

E_{0}

are constants. Initially the particle was at rest at

x = 0

. Other than the initial position the kinetic energy of the particle becomes zero when the distance of the particle from the origin is :

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A body of mass

m = 10^{- 2} kg

is moving in a medium and experiences a frictional force

F = - k v^{2} .

Its initial speed is

v_{0} = 10 m s^{- 1} .

After

10 s

its kinetic energy is

\frac{1}{8} m v_{0}^{2},

then value of

k

will be:-

EASY

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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?

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Two bodies A and B have masses in the ratio

5 : 1

and their kinetic energies are in the ratio

125 : 9

. Find the ratio of their velocities.

What is the work to be done to increase the velocity of a car from 36 kmh-1 to 72 kmh-1 if the mass of the car is 1500 kg?

Important Questions on Work and Energy

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What is the work to be done to increase the velocity of a car from $36 {kmh}^{- 1}$ to $72 {kmh}^{- 1}$ if the mass of the car is $1500 kg$ ?