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

EASY

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The total work done on a particle is equal to the change in its kinetic energy :-

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Important Questions on Laws of Motion

EASY

Physics>Mechanics>Laws of Motion>Work Energy Theorem

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>Laws of Motion>Work Energy Theorem

The only force acting on a $2 kg$ body that is moving in $x y$ -plane has a magnitude of $5 N$ . The body initially has a velocity of $4 m / s$ in the positive $x$ -direction. Some time later, the body has a velocity of $6 m / s$ in the positive $y$ -direction. The work done on the body by the $5 N$ force during this time is

EASY

Physics>Mechanics>Laws of Motion>Work Energy Theorem

The graph between resistive force $F$ acting on a body and the distance covered by the body is shown in the figure. If the mass and initial velocity of the body are $25 kg$ and $2 m \cdot s^{- 1}$ respectively, find its kinetic energy after having travelled a distance of $4 m$

Question Image

EASY

Physics>Mechanics>Laws of Motion>Work Energy Theorem

A ball of mass

m

is thrown upward with a velocity

v

. If air exerts an average resisting force

F,

the velocity with which the ball returns to the thrower is

EASY

Physics>Mechanics>Laws of Motion>Work Energy Theorem

A bullet of mass

5 g

, travelling with a speed of

210 m s^{- 1}

strikes a fixed wooden target. One half of its kinetic energy is converted into heat in the wood. The rise of temperature of the bullet if the specific heat of its material is

0.030 {(g ° C)}^{- 1} (1 calorie = 4 .2 \times 10^{7} ergs)

close to :

EASY

Physics>Mechanics>Laws of Motion>Work Energy Theorem

When work done by force of gravity is negative, then

EASY

Physics>Mechanics>Laws of Motion>Work Energy Theorem

A porter lifts a heavy suitcase of mass

80 kg

and at the destination lowers it down by a distance of

80 cm

with a constant velocity. Calculate the work done by the porter in lowering the suitcase. (take

g = 9.8 {ms}^{- 2}

)

MEDIUM

Physics>Mechanics>Laws of Motion>Work Energy Theorem

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

Physics>Mechanics>Laws of Motion>Work Energy Theorem

Which of the following statements is false?

EASY

Physics>Mechanics>Laws of Motion>Work Energy Theorem

A block of

10 kg

is sliding at an initial velocity of

5 m s^{- 1}

along the horizontal surface to the right. The surface has a coefficient of kinetic friction

0.3

. The distance to which the block will slide before coming to rest is (Assume

g = 10 m s^{- 2}

)

EASY

Physics>Mechanics>Laws of Motion>Work Energy Theorem

The potential energy stored in a spring when compressed by a length ‘x’ is

\frac{1}{2} {kx}^{2}

and the force required to compress it is

kx

;

k

is a constant of the spring known as spring constant.The spring is placed on a floor upright and a stone of mass

10 kg

falls and hits the spring with a speed

10 {ms}^{- 1}

. The spring is compressed by

5 cm

. Assuming that there is no loss of energy, what is the value of

k

? (Given: acceleration due to gravity is

10 {ms}^{- 2}

)

EASY

Physics>Mechanics>Laws of Motion>Work Energy Theorem

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

HARD

Physics>Mechanics>Laws of Motion>Work Energy Theorem

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>Laws of Motion>Work Energy Theorem

In the arrangement shown in the figure, $m_{A} = 1 kg$ and $m_{B} = 4 kg .$ Assume that the string is light and inextensible and the pulley is smooth. If the coefficient of friction between block $' A'$ and the table is $0.2,$ the speed of both the blocks when $' B'$ has descended through a height $h = 1 m$ is nearly take $(g = 10 m \cdot s^{- 2})$

Question Image

MEDIUM

Physics>Mechanics>Laws of Motion>Work Energy Theorem

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:

EASY

Physics>Mechanics>Laws of Motion>Work Energy Theorem

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

MEDIUM

Physics>Mechanics>Laws of Motion>Work Energy Theorem

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

Physics>Mechanics>Laws of Motion>Work Energy Theorem

The angular retardation of a rotating flywheel is proportional to the angle through which it rotates. If its kinetic energy gets reduced by

Δ E

while it rotates through an angle

θ,

then

EASY

Physics>Mechanics>Laws of Motion>Work Energy Theorem

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

Physics>Mechanics>Laws of Motion>Work Energy Theorem

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?

The total work done on a particle is equal to the change in its kinetic energy :-

Important Questions on Laws of Motion

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