MCQ Questions for Class 11 Engineering Physics Work,Energy And Power Quiz 3

One end of a light spring constant $$k$$ is fixed to a wall and the other end is tied to a block placed on a smooth horizontal surface. In a displacement, the work done by the spring is $$\frac {1}{2} kx^{2}$$. The possible cases are

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The spring was initially compressed by a distance $$x$$ and was finally in its natural length
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It was initially stretched by a distance $$x$$ and finally was in its natural length
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It was initially in its natural length and finally in a compressed position
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It was initially in its natural length and finally in a stretched position

A locomotive of mass $$m$$ has a velocity $$v = a \sqrt{x}$$. Find the work done by all the forces acting on locomotive in first $$t$$ sec.

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$$\displaystyle \frac{ma^2 t^2}{4}$$
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$$\displaystyle \frac{ma^4 t^2}{4}$$
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$$\displaystyle \frac{ma^4 t^2}{8}$$
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$$\displaystyle \frac{ma^4 t^2}{2}$$

Let $$\theta$$ denote the angular displacement of a simple pendulum oscillating in a vertical plane. If the mass of the bob is m, then tension in the string is mg $$\cos\theta$$

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always
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never
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at the extreme position
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at the mean position

Water in a bucket is whirled in a vertical circle with a string to it. The water does not fallen even when the bucket is inverted at the top of its path . We conclude that in this position:

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$$\displaystyle mg = \frac{mv^2}{r}$$
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$$mg$$ is greater than $$\displaystyle \frac{mv^2}{r}$$
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$$mg$$ is not greater than $$\displaystyle \frac{mv^2}{r}$$
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$$mg$$ is not less than $$\displaystyle \frac{mv^2}{r}$$

A ball with velocity $$9\ m/s$$ collides with another similar stationary ball. After the collision the two balls move in directions making an angle of $$30^o$$ with the initial direction. The ratio of the speeds of balls after the collision will be :

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$$\displaystyle \dfrac{v_1}{v_2} = 1$$
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$$\displaystyle \dfrac{v_1}{v_2} > 1$$
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$$\displaystyle \dfrac{v_1}{v_2} < 1$$
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$$\displaystyle \dfrac{v_1}{v_2} = 0$$

A particle P of mass m attached to a vertical axis by two strings AP and BP of length 1m each. The separation $$AB = l$$. P rotates around the axis with an angular velocity $$\omega$$. The tension in the two strings are $$T_1$$ and $$T_2$$.

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$$T_1 = T_2$$
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$$T_1 + T_2 = m\omega^2l$$
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$$T_1 - T_2 = 2mg$$
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BP will remain taut only if $$\omega \ge \sqrt{2g/l}$$

A stone of mass $$1000g$$ tied to a light string of length $$10/3m$$ is whirling in a vertical circle. If the ratio of the maximum tension to minimum tension is $$4$$ and $$g=10{ ms }^{ -2 }$$, then the speed of stone at the highest point of circle is :

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$$20{ ms }^{ -1 }$$
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$$10\sqrt { 3 } { ms }^{ -1 }$$
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$$5\sqrt { 3 } { ms }^{ -1 }$$
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$$10{ ms }^{ -1 }$$

A toy car is tied to the end of an unstretched string of a length, $$a$$. When revolved, the toy car moves in a horizontal circle of radius $$2a$$ with time period, $$T$$. If it is now revolved in a horizontal circle of radius $$3a$$ with a period $$T'$$ with the same force, then

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$$\displaystyle T' = \dfrac{\sqrt{3}}{2} T$$
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$$\displaystyle T' = \sqrt {\dfrac{3}{2}} T$$
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$$T' = T$$
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$$\displaystyle T' = \dfrac{3}{2} T$$

In the elastic collision of heavy vehicle moving with a velocity 10 ms$$^{-1}$$ and a small stone at rest, the stone will fly away with a velocity equal to :

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40 ms$$^{-1}$$
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20 ms$$^{-1}$$
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10 ms$$^{-1}$$
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5 ms$$^{-1}$$

A sphere of mass m, moving with a speed v, strikes a wall elastically at an angle of incidence $$\theta$$. If the speed of the sphere before and after collision is the same and the angle of incidence and velocity normally towards the wall the angle of rebound is equal to the angle of incidence and velocity normally towards the wall is taken as negative then, the change in the momentum parallel to wall is :

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mv cos $$\theta$$
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2mv cos $$\theta$$
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-2mv cos $$\theta$$
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zero

A body of mass $$1\ kg$$ is rotating in a vertical circle of radius $$1\ m$$. What will be the difference in its kinetic energy at the top and bottom of the circle?

Take $$g = 10\ m/s^{2}$$

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$$50\ J$$
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$$30\ J$$
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$$20\ J$$
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$$10\ J$$

The work done in stretching a spring of force constant $$K$$ from length $$l_1$$ to $$l_2$$ is :

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$$K (l_2 - l_1)$$
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$$\displaystyle \frac{K}{2} (l_2 + l_1)$$
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$$K (l_2^2 - l_1^2)$$
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$$\displaystyle \frac{K}{2} (l_2^2 - l_1^2)$$

A ball of mass $$m$$ moving with velocity $$v$$ collides elastically with wall and rebounds. The change in momentum of the ball will be :

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$$4 mv$$
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$$2 mv$$
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$$mv$$
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$$zero$$

The velocity of a particle at highest point of the vertical circle is $$\sqrt{3rg}$$. The tension at the lowest point, if mass of the particle is $$m$$, is

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$$2\ mg$$
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$$4\ mg$$
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$$6\ mg$$
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$$8\ mg$$

A stone of mass $$1\ kg$$ is tied of the end of a string $$1\ m$$ long. It is whirled in a vertical circle. If the velocity of stone at the top is $$4\ m/s$$. What is the tension in the string at the lowest point?

Take $$g = 10\ m/s^{2}$$

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$$6\ N$$
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$$66\ N$$
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$$5.2\ N$$
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$$76\ N$$

A bullet weighing 10 g and moving at 300 ms$$^{-1}$$ strikes a 5 kg block of ice and drops dead. The ice block is sitting on frictionless level surface. The speed of the block, after the collision is :

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60 ms$$^{-1}$$
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3 ms$$^{-1}$$
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6 ms$$^{-1}$$
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0.6 ms$$^{-1}$$

A massive ball moving with a speed $$v$$ collide with a tiny ball having a very small mass , immediately after the impact the second ball will move at speed approximately equal to :

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$$\infty$$
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$$\dfrac{v}{2}$$
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$$v$$
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$$2v$$

A spring of spring constant $$5\times 10^3N/m$$ is stretched initially by 5 cm from the unstretched position. Then the work required to stretch it further by another 5 cm is

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$$18.75 J$$
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$$25.00 J$$
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$$6.25 J$$
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$$12.50 J$$

A pump is used to lift $$500\ kg$$ of water from a depth of $$80\ m$$ in $$10\ s$$.

(Take $$g=10\ ms^{-2}$$). Calculate the work done by the pump.

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$$16 \times 10^5J$$
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$$4\times 10^5J$$
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$$4\times 10^8J$$
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$$2\times 10^5J$$

What will be the potential energy of a body of mass 5 kg kept at a height of 10 m ?

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50 J
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0.5 J
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500 J
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25 J

A particle moves under the effect of a force $$F=cx$$ from $$x=0$$ to $$x=x_1$$, the work done in the process is

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$$cx_1^2$$
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$$\displaystyle \frac{1}{2} cx_1^2$$
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$$2cx_1^2$$
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zero

Two solid rubber balls $$A$$ and $$B$$ having masses $$200\ \&\ 400\ \text{gm}$$ respectively are moving in opposite direction with velocity of $$A$$ equal to $$0.3\ \text{m/sec}.$$ After collision the two balls come to rest when the velocity of $$B$$ is :

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$$0.15\ \text{m/sec}$$
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$$1.5\ \text{m/sec}$$
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$$-0.15\ \text{m/sec}$$
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$$\text{None of these}$$

Name the type of energy (kinetic energy $$K$$ or potential energy $$U$$) possessed in the following case.

The bob of a simple pendulum at its extreme position.

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$$K$$
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$$U$$
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$$K$$ and $$U$$
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No energy

A man raises a box of mass $$50 \ kg$$ to a height of $$2 \ m$$ in $$2 \ minutes$$, while another man raises the same box to the same height in $$5 \ minutes$$. What is the ratio of work done by them ?

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$$1 : 1$$
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$$2 : 1$$
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$$1 : 2$$
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$$4 : 1$$

Two objects that are moving along an xy-plane on a frictionless floor collide. Assume that they form a closed, isolated system. The following table gives some of the momentum components (in kilogram meters per second) before and after the collision. What are the mission values (a, b):

	Before collision		After collision
Object	P$$_x$$	P$$_y$$	P$$_x$$	P$$_y$$
A	-4	5	3	a
B	b	-2	4	2

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10, 11
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1, 11
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5, 7
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6, 4

The hydroelectric plants do not produce electricity, if the water level in the dam is less than 34 m.

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True
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False
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Ambiguous
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Data insufficient

A block is acted upon by a force, which is inversely proportional to the displacement $$x$$. The work done will be proportional to

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$$x$$
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$$x^{1/2}$$
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$$x^2$$
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none of these

A small sphere is attached to a cord and rotates in a vertical circle about a point $$O$$. If the average speed of the sphere is increased, the cord is most likely to break at the orientation when the mass is at

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Bottom point $$B$$
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Top point $$A$$
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Point $$D$$
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Point $$C$$

Name the type of energy (kinetic energy $$K$$ or potential energy $$U$$) possessed in the following case.

A piece of stone placed on the roof.

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$$U$$
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$$K$$
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$$U$$ and $$K$$
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No energy

During the displacement, which of the curves shown in the graph best represents the work done on the spring block system by the applied force ?

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1
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2
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3
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4

By stretching the rubber strings of a catapult we store .......... energy in it.

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$$potential$$
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$$electrical$$
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$$heat$$
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$$kinetic$$

A body starts from rest and acquires a velocity $$V$$ in time $$T$$ at constant rate. The work done on the body in time $$t$$ will be proportional to

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$$\displaystyle \frac{V}{T}t$$
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$$\displaystyle \frac{V^2}{T}t^2$$
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$$\displaystyle \frac{V^2}{T^2}t$$
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$$\displaystyle \frac{V^2}{T^2}t^2$$

A simple pendulum is vibrating with angular amplitude of $$\theta=90^{o}$$ as shown in figure.
For what value of $$\theta$$ is the acceleration directed
$$(i)$$ Vertically upwards
$$(ii)$$ Horizontally
$$(iii)$$ Vertically downwards

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$$0^{o},90^{o} \ cos^{-1}\displaystyle\frac{1}{\sqrt {3}},\ 90^{o}$$
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$$ \cos^{-1}\displaystyle\frac{1}{\sqrt {3}},\ ,\ 0^{o},90^{o}$$
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$$0^{o},90^{o}, \cos^{-1}\displaystyle\frac{1}{\sqrt{2}},$$
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$$ \cos^{-1}\displaystyle\frac{1}{\sqrt {3}},\ 90^{o},\ 0^{o}$$

A stone tied to a string of length $$L$$ is swired in a verticle circle with the other end of the string at the centre. At a certain instant of time the stone is at it lowest position and has a speed $$u$$. Find the magnitude of the change in its velocity as it reaches a position, where the string is horizontal.

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$$\displaystyle \sqrt{(u^{2}-gL)}$$
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$$\displaystyle \sqrt{2(u^{2}-gL)}$$
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$$\displaystyle \sqrt{(u^{2}-2gL)}$$
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$$\displaystyle \sqrt{2(u^{2}-2gL)}$$

A spring of force constant k is cut in two parts at its one-third length. When both the parts are stretched by same amount. The work done in the two parts will be:
(Note- Spring constant of a spring is inversely proportional to length of spring.)

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equal in both
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greater for the longer part
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greater for the shorter part
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data insufficient

A spring of force constant $$800\ N/m$$ has an extension of $$5\ cm$$. The work done in extending it from $$5\ cm$$ to $$15\ cm$$ is

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$$16\ J$$
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$$8\ J$$
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$$32\ J$$
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$$24\ J$$

A pendulum bob is raised to a height, $$h$$, and released from rest. At what height will it attain half of its maximum speed?

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$$\displaystyle\frac{3h}{4}$$
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$$\displaystyle\frac{h}{2}$$
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$$\displaystyle\frac{h}{4}$$
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$$0.707h$$

A simple pendulum of length $$l$$ has maximum angular displacement $$\displaystyle \theta .$$ Then maximum kinetic energy of a bob of mass $$m$$ is

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$$\displaystyle \frac{1}{2}mgl$$
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$$\displaystyle \frac{1}{2}mgl\cos \theta $$
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$$\displaystyle mgl\left ( 1-\cos \theta \right )$$
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$$\displaystyle \frac{1}{2}mgl\sin \theta $$

A particle of mass $$m$$ moves on a straight line with its velocity varying with the distance travelled according to the equation $$\displaystyle v= \alpha \sqrt{x},$$ where a is a constant. Find the total work done by all the forces during a displacement from $$x=0$$ to $$x=d$$.

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$$\displaystyle \frac{1}{2}ma ^{2}b$$
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$$\displaystyle \frac{1}{4}ma ^{2}b$$
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$$ma ^{2}b$$
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$$2\ ma ^{2}b$$

A block of mass $$m=2$$ kg is pulled by a force $$F=40$$ N upwards through a height $$h=2 m$$. Find the work done on the block by the applied force F and its weight mg. $$\displaystyle \left ( g= 10 m/s^{2} \right )$$

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$$\displaystyle W_F = 80 J;W_{mg}= -40 J$$
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$$\displaystyle W_F = 80 J;W_{mg}= 40 J$$
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$$\displaystyle W_F = -80 J;W_{mg}= -40 J$$
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$$\displaystyle W_F = -80 J;W_{mg}= 40 J$$

A force $$F$$ acting on a particle varies with the position $$x$$ as shown in figure. Find the work done by this force in displacing the particle from $$\displaystyle x= 0\ m\:to\:x= 2\ m.$$

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$$-10J$$
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$$10J$$
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$$5J$$
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$$-5J$$

A block is constrained to move along x-axis under a force F=-2x. Here, F is in newton and x in metre. Find the work done by this force when the block is displaced from x=2 m to x=-4 m.

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-4 J
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-8 J
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-12 J
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-16 J

A bob is suspended from a crane by a cable of length $$5m$$. The crane and load are moving at a constant speed $$v_{0}$$. The crane is stopped by a bumper and the bob on the cable swings out an angle of $$60^{\circ}$$. Find the initial speed $$v_{0}.(g=9.8 m/s^{2})$$

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$$2 ms^{-1}$$
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$$3 ms^{-1}$$
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$$5 ms^{-1}$$
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$$7 ms^{-1}$$

A force $$F=(2+x)$$ acts on a particle in x-direction where $$F$$ is in newton and $$x$$ in meter. Find the work done by this force during a displacement from $$x=1.0$$ m to $$x=2.0\ m$$.

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$$3.5 \ J$$
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$$7 \ J$$
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$$4.5 \ J$$
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$$5.5 \ J$$

A force $$\displaystyle \vec{F}= \left ( 3t\hat{i}+5\hat{j} \right )N$$ acts on a body due to which its displacement varies as $$\displaystyle \vec{S}= \left ( 2t^{2}\hat{i}-5\hat{j} \right )m.$$ Work done by this force in 2 second is:

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32 J
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24 J
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46 J
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20 J

A block is constrained to move along x-axis under a force $$\displaystyle F= \frac{4}{x^{2}}\left ( x\neq 0 \right ).$$ Here, F is in newton and x in metre. Find the work done by this force when the block is displaced from x=4 m to x=2 m.