EASY

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If a variable force $F$ acting on an object varies with distance $x$ as shown in the figure, what is the work done by the force in moving the object from $x = 0$ to $x = 20 m$ ?

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Important Questions on Laws of Motion

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:

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

Arrange the four graphs in descending order of total work done; where $W_{1}, W_{2}, W_{3}$ and $W_{4}$ are the work done corresponding to figure $a, b, c$ and $d$ respectively.

HARD

Physics>Mechanics>Laws of Motion>Work and Energy

A force of

F = (5 y + 20) \hat{j} N

acts on a particle. The work done by this force when the particle is moved from

y = 0 m

y = 10 m

is ________

J

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)

HARD

Physics>Mechanics>Laws of Motion>Work and Energy

A particle is moved along a path

A B - B C - C D - D E - E F - F A,

as shown in figure, in presence of a force

\vec{F} = (α y \hat{i} + 2 α x \hat{j}) N,

where

x

and

y

are in meter and

α = - 1 N m^{- 1} .

The work done on the particle by this force

\vec{F}

will be ____ Joule.

MEDIUM

Physics>Mechanics>Laws of Motion>Work and Energy

The relationship between the force

F

and position

x

of a particle is as shown in the following diagram. The work done in displacing the particle from

x = 0 m

5 m

will be:

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

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

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

EASY

Physics>Mechanics>Laws of Motion>Work and Energy

A force

F = (5 + 3 y^{2})

acts on a particle in the

y

-direction, where

F

is newton and

y

is in meter. The work done by the force during a displacement from

y = 2 m

y = 5 m

is ______

J

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

A force

\vec{F} = (2 + 3 x) \hat{i}

acts on a particle in the

x

direction where

F

is in Newton and

x

is in meter. The work done by this force during a displacement from

x = 0

x = 4 m

is _____

J

EASY

Physics>Mechanics>Laws of Motion>Work and Energy

A variable force

F = 5 K x N

acts on a body moving along x-axis. Find the work done by this force in displacing the body from

x = 2 m

x = 5 m

(

K

is a constant).

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:

EASY

Physics>Mechanics>Laws of Motion>Work and Energy

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?

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

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

EASY

Physics>Mechanics>Laws of Motion>Work and Energy

A force

F = 20 + 10 y

acts on a particle in

y

-direction where

F

is in Newton and

y

is in meter. Work done by this force to move the particle from

y = 0

y = 1 m

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 :

If a variable force F acting on an object varies with distance x as shown in the figure, what is the work done by the force in moving the object from x=0 to x=20 m?

Important Questions on Laws of Motion

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If a variable force $F$ acting on an object varies with distance $x$ as shown in the figure, what is the work done by the force in moving the object from $x = 0$ to $x = 20 m$ ?