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The relationship between the force $F$ and position $x$ of a body is as shown in figure. Then what will be the work done in displacing the body from $x = 1 m$ to $x = 5 m$ ?

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Important Questions on Laws of Motion

MEDIUM

Physics>Mechanics>Laws of Motion>Work and Energy

Consider a force

\vec{F} = - x \hat{i} + y \hat{j}

. The work done by this force in moving a particle from point

A (1,0)

B (0,1)

along the line segment is : (all quantities are in SI units)

MEDIUM

Physics>Mechanics>Laws of Motion>Work and Energy

The work done on a particle of mass

m

by a force

K [\frac{x}{{(x^{2} + y^{2})}^{3 / 2}} \hat{i} + \frac{y}{{(x^{2} + y^{2})}^{3 / 2}} \hat{j}]

(

K

being a constant of appropriate dimensions, when the particle is taken from the point

(a, 0)

to the point

(0, a)

along a circular path of radius

a

about the origin in the x-y plane is

EASY

Physics>Mechanics>Laws of Motion>Work and Energy

The work done to raise a mass

m

from the surface of the earth to a height

h

, which is equal to the radius of the earth is:

MEDIUM

Physics>Mechanics>Laws of Motion>Work and Energy

The work done by a force

\vec{F} = - 5 x^{4} \hat{i} N

in displacing a body from

x = 2 m

x = - 2 m

MEDIUM

Physics>Mechanics>Laws of Motion>Work and Energy

Two similar springs

P

and

Q

have spring constants

K_{P}

and

K_{Q}

, such that

K_{P} > K_{Q}

. They are stretched, first by the same amount (case a), then by the same force (case b). the work done by the springs

W_{P}

and

W_{Q}

are related as respectively, in case

EASY

Physics>Mechanics>Laws of Motion>Work and Energy

A particle of mass

10 g

is thrown vertically upwards with a speed of

20 m s^{- 1}

. The work done by the gravitational force during the time the particle moves upward is

HARD

Physics>Mechanics>Laws of Motion>Work and Energy

A point particle of mass m, moves along the uniformly rough track PQR as shown in the figure. The coefficient of friction, between the particle and the rough track equals

μ

. The particle is released, from rest, from the point P and it comes to rest at a point R. The energies, lost by the ball, over the parts, PQ and QR, of the track, are equal to each other, and no energy is lost when particle changes direction from PQ to QR.
The values of the coefficient of friction

μ

and the distance

x = (Q R)

, are respectively close to:

MEDIUM

Physics>Mechanics>Laws of Motion>Work and Energy

A force

F = 3 x^{2} + 2 x + 1

acts on a body in the

x

-direction. The work done by this force during a displacement from

x = - 1

+ 1

MEDIUM

Physics>Mechanics>Laws of Motion>Work and Energy

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:

MEDIUM

Physics>Mechanics>Laws of Motion>Work and Energy

A block of mass $m$ slides from rest at a height $H$ on a frictionless inclined plane as shown in the figure. It travels a distance $d$ across a rough horizontal surface with coefficient of kinetic friction $μ$ and compresses a spring of spring constant $k$ by a distance $x$ before coming to rest momentarily. Then the spring extends and the block travels back attaining a final height of $h$ .

Then

EASY

Physics>Mechanics>Laws of Motion>Work and Energy

If reaction is $R$ and coefficient of friction $μ_{r}$ what is the work done against friction in moving a body by distance $d$ ?

MEDIUM

Physics>Mechanics>Laws of Motion>Work and Energy

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,

EASY

Physics>Mechanics>Laws of Motion>Work and Energy

Work done in sliding a

1 kg

block up a rough inclined plane of height

5 m

100 J .

Work done against the friction is

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

EASY

Physics>Mechanics>Laws of Motion>Work and Energy

When a rubber string is stretched through a distance

x

, the restoring force developed has a magnitude

(p x + q x^{2} + r x^{3})

where

p, q

and

r

are constants. Work done in stretching the unstretched rubber string by a distance

l

, is

EASY

Physics>Mechanics>Laws of Motion>Work and Energy

A cyclist comes to a skidding stop in

10 m

. During this process, the force on the cycle due to the road is

200 N

and is directly opposed to the motion. How much work does the road do on the cycle?

EASY

Physics>Mechanics>Laws of Motion>Work and Energy

When a force

\vec{F} = 17 - 2 x + 6 x^{2} N

acts on a body of mass

2 kg

and displaces it from

x = 0 m

x = 8 m

, the work done is

MEDIUM

Physics>Mechanics>Laws of Motion>Work and Energy

A body of mass

m

dropped from a height

h

reaches the ground with a speed of

0.8 \sqrt{g h} .

The value of work done by the air-friction is:

MEDIUM

Physics>Mechanics>Laws of Motion>Work and Energy

Consider a drop of rain water having mass

1 g

falling from a height of

1 km

. It hits the ground with a speed of

50 m s^{- 1}

. Take

g

constant with a value

10 m s^{- 2}

. The work done by the (i) gravitational force and the (ii) resistive force of air is

MEDIUM

Physics>Mechanics>Laws of Motion>Work and Energy

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>Laws of Motion>Work and Energy

A block of mass

m,

lying on a smooth horizontal surface, is attached to a spring (of negligible mass) of spring constant

k .

The other end of the spring is fixed, as shown in the figure. The block is initially at rest in its equilibrium position. If now the block is pulled with a constant force

F,

the maximum speed of the block is:

The relationship between the force F and position x of a body is as shown in figure. Then what will be the work done in displacing the body from x=1 m to x = 5 m ?

Important Questions on Laws of Motion

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The relationship between the force $F$ and position $x$ of a body is as shown in figure. Then what will be the work done in displacing the body from $x = 1 m$ to $x = 5 m$ ?