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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

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

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:
           

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

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. \(1:\sqrt{3}\)

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. \(mg(h-d)+\frac{1}{2}kd^2\)

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. \(Mg/2k\)

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)$\frac{1}{2}\frac{m{v}^2}{t_1^2}{t}^2$