Work, Energy & Power - Live Session

A body moves a distance of 10 m along a straight line under the action of a force of 5 N. If the work is done is 25 joules, the angle which the force makes with the direction of motion of the body is
1. 0 $°$
2. 30 $°$
3. 60 $°$
4. 90 $°$

A force acts on a 30 gm particle in such a way that the position of the particle as a function of time is given by $x = 3 t - 4 t^{2} + t^{3}$ , where x is in metres and t is in seconds. The work done during the first 4 seconds is
1. 5.28 J
2. 450 J
3. 490 J
4. 530 mJ

A particle moves from position $\vec{r_{1}} = 3 \hat{i} + 2 \hat{j} - 6 \hat{k}$ to position $\vec{r_{2}} = 14 \hat{i} + 13 \hat{j} + 9 \hat{k}$ under the action of force $4 \hat{i} + \hat{j} + 3 \hat{k}$ N. The work done will be
1. 100 J
2. 50 J
3. 200 J
4. 75 J

A force $(\vec{F}) = 3 \hat{i} + c \hat{j} + 2 \hat{k}$ acting on a particle causes a displacement: $(\vec{s}) = - 4 \hat{i} + 2 \hat{j} + 3 \hat{k}$ in its own direction. If the work done is 6 J, then the value of 'c' is
1. 0
2. 1
3. 6
4. 12

A ball is released from the top of a tower. The ratio of work done by a force of gravity in first, second and third second of the motion of the ball is
1. 1 : 2 : 3
2. 1 : 4 : 9
3. 1 : 3 : 5
4. 1 : 5 : 3

A cord is used to lower vertically a block of mass M by a distance d with constant downward acceleration $\frac{g}{4}$ . Work done by the cord on the block is
1. $M g \frac{d}{4}$
2. 3 $m g \frac{d}{4}$
3. -3 $m g \frac{d}{4}$
4. Mgd

The potential energy of a certain spring, when stretched through a distance 'S', is 10 joule. The amount of work (in joule) that must be done on this spring to stretch it through an additional distance 'S' will be
1. 30
2. 40
3. 10
4. 20

A position-dependent force $F = 7 - 2 x + 3 x^{2}$ newton acts on a small body of mass 2 kg and displaces it from x = 0 to x = 5 m. The work done in joules is
1. 70
2. 270
3. 35
4. 135

The potential energy between two atoms in a molecule is given by U(x) = $\frac{a}{x^{12}} - \frac{b}{x^{6}}$ ; Where a and b are positive constants and x is the distance between the atoms. The
atom is in stable equilibrium when
1. $x = \sqrt[6]{\frac{11 a}{5 b}}$
2. $x = \sqrt[6]{\frac{a}{2 b}}$
3. x=0
4. x $= \sqrt[6]{\frac{2 a}{b}}$

10.

A running man has half the kinetic energy of that of a boy of half of his mass. The man
speeed up by 1m/s so as to have same K.E. as that of the boy. The original speed of
the man will be
1. $\sqrt{2} m / s$
2. $(\sqrt{2} - 1) m / s$
3. $\frac{1}{\sqrt{2 - 1}} m / s$
4. $\frac{1}{\sqrt{2}} m / s$

11.

A particle of mass m at rest is acted upon by a force F for a time t. its Kinetic energy after an interval t is
1.   $\frac{F^{2} t^{2}}{m}$
2.   $\frac{F^{2} t^{2}}{2 m}$
3.   $\frac{F^{2} t^{2}}{3 m}$
4.   $\frac{F t}{2 m}$

12.

A block of mass $m$ initially at rest is dropped from a height $h$ on to a spring of force constant $k$ . the maximum compression in the spring is $x$ then

(1) $m g h = \frac{1}{2} k x^{2}$
(2) $m g (h + x) = \frac{1}{2} k x^{2}$
(3) $m g h = \frac{1}{2} k {(x + h)}^{2}$
(4) $m g (h + x) = \frac{1}{2} k {(x + h)}^{2}$

13.

A spherical ball of mass 20 kg is stationary at the top of a hill of height 100m. It slides down a smooth surface to the ground, then climbs up another hill of height 30m and finally slides down to a horizontal base at a height of 20m above the ground. The velocity attained by the ball is
1. 10 m/s
2. $10 \sqrt{3}$ m/s
3. 40 m/s
4. 20 m/s

14.

A body of mass m accelerates uniformly from rest to V $_{1}$ in time t $_{1}$ .As a function to time t, the instantaneous power delivered to the body is
1. $\frac{m v_{1} t}{t_{1}}$
2. $\frac{m v_{1}^{2} t}{t_{1}}$
3. $\frac{m v_{1} t^{2}}{t_{1}}$
4. $\frac{m {v_{1}}^{2} t}{{t_{1}}^{2}}$

15.

A weight lifter lifts 300 kg from the ground to a height of 2 meters in 3 seconds. The average power generated by him is
1. 5880 watt
2. 4410 watt
3. 2205 watt
4. 1960 watt

16.

An engine pump is used to pump liquid of density $ρ$ continuously through a pipe of cross-sectional area A. If the speed of flow of the liquid in the pipe is v, then the rate at which kinetic energy is being imparted to the liquid is
1.   $\frac{1}{2} A ρ ν^{3}$
2.   $\frac{1}{2} A ρ ν^{2}$
3.   $\frac{1}{2} A ρ ν$
4.   $A ρ ν$

17.

A uniform chain of length L and mass M is lying on a smooth table and one-third of its length is hanging vertically down over the edge of the table. If g is the acceleration due to gravity, the work required to pull the hanging part on to the table is
1. Mg/L
2. MgL/3
3. MgL/9
4. MgL/18

18.

If $W_{1}$ , $W_{2}$ and $W_{3}$ represent the work done in moving a particle from A to B along three different paths 1, 2 and 3 respectively (as shown) in the gravitational field of a point mass m, find the correct relation between $W_{1}$ , $W_{2}$ and $W_{3}$

1. $W_{1}$ > $W_{2}$ > $W_{3}$
2.   $W_{1}$ = $W_{2}$ = $W_{3}$
3.   $W_{1}$ < $W_{2}$ < $W_{3}$
4.   $W_{2}$ > $W_{1}$ > $W_{3}$

19.

The displacement x of a particle x of a particle moving in one dimension under the action of a constant force is related to the time t by the equation $t = \sqrt{x} + 3$ where x is in meters and t is in seconds. The work done by the force in the first 6 seconds is
1. 9 J
2. 6 J
3. 0 J
4. 3 J

20.

An open knife-edge of mass 'm' is dropped from a height 'h' on a wooden floor. If the blade penetrates upto the depth 'd' into the wood, the average resistance offered by the wood to the knife-edge is
1. mg
2.   $m g (1 - \frac{h}{d})$
3.   $m g (1 + \frac{h}{d})$
4.   $m g {(1 + \frac{h}{d})}^{2}$

21.

A toy car of mass 5 kg moves up a ramp under the influence of force F plotted against displacement x. The maximum height attained is given by

1.   $y_{m a x}$ = 20m
2.   $y_{m a x}$ = 15m
3.   $y_{m a x}$ = 11m
4.   $y_{m a x}$ = 5m

22.

A particle of mass 0.1 kg is ubjected to a force which varies with distance as shown in fig. If it starts its journey from rest at x = 0, its velocity at x = 12m is

1. o m/s
2. $20 \sqrt{2} m / s$
3. $20 \sqrt{3} m / s$
4. 40 m/s

23.

The potential energy of a particle varies with distance x as shown in the graph.

The force acting on the particle is zero at
1. C
2. B
3. B and C
4. A and D

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