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A particle starts to move along the path which locus is given as $x^{2} = (8 y)$ $(x & y are in m)$ , due to applied force $\vec{F} = (a x \hat{i} + b y \hat{j}) N$ $(a > 0 and b > 0 and x & y are in metre)$ . The amount of work done in displacing particle from $x = 0$ to $x = 1$ metre is

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Important Questions on Work, Energy and Power

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Physics>Mechanics>Work, Energy and Power>Work Done by a Variable Force

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.
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HARD

Physics>Mechanics>Work, Energy and Power>Work Done by a Variable Force

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:

Question Image

EASY

Physics>Mechanics>Work, Energy and Power>Work Done by a Variable Force

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:

EASY

Physics>Mechanics>Work, Energy and Power>Work Done by a Variable Force

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

MEDIUM

Physics>Mechanics>Work, Energy and Power>Work Done by a Variable Force

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>Work, Energy and Power>Work Done by a Variable Force

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>Work, Energy and Power>Work Done by a Variable Force

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

HARD

Physics>Mechanics>Work, Energy and Power>Work Done by a Variable Force

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>Work, Energy and Power>Work Done by a Variable Force

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 $h$ .

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Then

MEDIUM

Physics>Mechanics>Work, Energy and Power>Work Done by a Variable Force

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>Work, Energy and Power>Work Done by a Variable Force

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>Work, Energy and Power>Work Done by a Variable Force

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 :

EASY

Physics>Mechanics>Work, Energy and Power>Work Done by a Variable Force

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

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MEDIUM

Physics>Mechanics>Work, Energy and Power>Work Done by a Variable Force

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)

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EASY

Physics>Mechanics>Work, Energy and Power>Work Done by a Variable Force

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})

MEDIUM

Physics>Mechanics>Work, Energy and Power>Work Done by a Variable Force

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>Work, Energy and Power>Work Done by a Variable Force

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?

MEDIUM

Physics>Mechanics>Work, Energy and Power>Work Done by a Variable Force

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

MEDIUM

Physics>Mechanics>Work, Energy and Power>Work Done by a Variable Force

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>Work, Energy and Power>Work Done by a Variable Force

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,

A particle starts to move along the path which locus is given as x2=(8y) (x&y are in m), due to applied force F→=(axi^+byj^ ) N (a>0 and b>0 and x & y are in metre). The amount of work done in displacing particle from x=0 to x=1 metre is

Important Questions on Work, Energy and Power

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A particle starts to move along the path which locus is given as $x^{2} = (8 y)$ $(x & y are in m)$ , due to applied force $\vec{F} = (a x \hat{i} + b y \hat{j}) N$ $(a > 0 and b > 0 and x & y are in metre)$ . The amount of work done in displacing particle from $x = 0$ to $x = 1$ metre is