Work, Energy and power

1.

A body is acted upon by a force which is proportional to the distance covered. If distance covered be denoted by x, then work done by the force will be proportional to :-
(1) x
(2) $x^{2}$
(3) $x^{3 / 2}$
(4) none of these

2.

Work energy theorem is valid in
(1) Only inertial frame of reference
(2) The only non-inertial frame of reference
(3) Both inertial and non-inertial frame of reference
(4) Does not depend on any frame of reference

3.

An object of mass $500~\text g$ initially at rest is acted upon by a variable force whose $x$ -component varies with $x$ in the manner shown. The velocities of the object at the points $x=8~\text m$ and $x=12~\text m$ would have the respective values of nearly:

1.	$18~\text {m/s}$ and $22.4~\text {m/s}$	2.	$23~\text {m/s}$ and $22.4~\text {m/s}$
3.	$23~\text {m/s}$ and $20.6~\text {m/s}$	4.	$18~\text {m/s}$ and $20.6~\text {m/s}$

4.

A body of mass m dropped from a height H reaches
the ground with a speed of 1.2 $\sqrt{gH}$ . The work done
by air friction is
1. 0.14 mgH
2. 0.28 mgH
3. – 0.14 mgH
4. – 0.28 mgH

5.

When an object is shot from the bottom of a long, smooth inclined plane kept at an angle of $60^\circ$ with horizontal, it can travel a distance $x_1$ along the plane. But when the inclination is decreased to $30^\circ$ and the same object is shot with the same velocity, it can travel $x_2$ distance. Then $x_1:x_2$ will be:
1. $1:2\sqrt{3}$
2. $1:\sqrt{2}$
3. $\sqrt{2}:1$
4. $1:\sqrt{3}$

6.

A vertical spring with a force constant $k$ is fixed on a table. A ball of mass $m$ at a height $h$ above the free upper end of the spring falls vertically on the spring so that the spring is compressed by a distance $d$ . The net work done in the process is:
1. $mg(h+d)+\frac{1}{2}kd^2$
2. $mg(h+d)-\frac{1}{2}kd^2$
3. $mg(h-d)-\frac{1}{2}kd^2$
4. $mg(h-d)+\frac{1}{2}kd^2$

7.

A block of mass $M$ is attached to the lower end of a vertical spring. The spring is hung from the ceiling and has a force constant value of $k.$ The mass is released from rest with the spring initially unstretched. The maximum extension produced along the length of the spring will be:
1. $Mg/k$
2. $2Mg/k$
3. $4Mg/k$
4. $Mg/2k$

8.

Work done in time $t$ on a body of mass $m$ which is accelerated from rest to a speed $v$ in time $t_{1}$ as a function of time $t$ is given by
(a) $\frac{1}{2} m \frac{v}{t_{1}} t^{2}$
(b) $m \frac{v}{t_{1}} t^{2}$
(c) $\frac{m v^{2} t^{2}}{t_{1}}$
(d) $\frac{1}{2} \frac{m v^{2}}{t_{1}^{2}} t^{2}$

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