Consider a drop of rainwater having a mass of \(1~\text{gm}\) falling from a height of \(1~\text{km}\). It hits the ground with a speed of \(50~\text{m/s}\). Take \(g\)  as constant with a value \(10~\text{m/s}^2.\) The work done by the
(i) gravitational force and the
(ii) resistive force of air is:

1.	\((\text{i})~1.25~\text{J};\) \((\text{ii})~-8.25~\text{J}\)
2.	\((\text{i})~100~\text{J};\) \((\text{ii})~8.75~\text{J}\)
3.	\((\text{i})~10~\text{J};\) \((\text{ii})~-8.75~\text{J}\)
4.	\((\text{i})~-10~\text{J};\) \((\text{ii})~-8.75~\text{J}\)

A bullet of mass \(10\) g moving horizontal with a velocity of \(400\) m/s strikes a wood block of mass \(2\) kg which is suspended by light inextensible string of length \(5\) m. As a result, the centre of gravity of the block is found to rise a vertical distance of \(10\) cm. The speed of the bullet after it emerges horizontally from the block will be:

Two identical balls \(A\) and \(B\) having velocities of \(0.5~\text{m/s}\) and \(-0.3~\text{m/s}\), respectively, collide elastically in one dimension. The velocities of \(B\) and \(A\) after the collision, respectively, will be:

A moving block having mass \(m\) collides with another stationary block having a mass of \(4m.\) The lighter block comes to rest after the collision. When the initial velocity of the lighter block is \(v,\) then the value of the coefficient of restitution \((e)\) will be:
1. \(0.5\)
2. \(0.25\)
3. \(0.8\)
4. \(0.4\)

A body initially at rest and sliding along a frictionless track from a height \(h\) (as shown in the figure) just completes a vertical circle of diameter \(\mathrm{AB}= D.\) The height \({h}\) is equal to:
        
1. \({3\over2}D\)
2. \(D\)
3. \({7\over4}D\)
4. \({5\over4}D\)

What is the minimum velocity with which a body of mass \(m\) must enter a vertical loop of radius \(R\) so that it can complete the loop?
1. \(\sqrt{2 g R}\)
2. \(\sqrt{3 g R}\)
3. \(\sqrt{5 g R}\)
4. \(\sqrt{ g R}\)$\mathrm{}$

A ball is thrown vertically downward from a height of \(20\) m with an initial velocity \(v_0\). It collides with the ground, loses \(50\%\) of its energy in a collision, and rebounds to the same height. The initial velocity \(v_0\) is: 
(Take, \(g=10~\mathrm{ms^{-2}}\))
1. \(14\) ms^–1
2. \(20\) ms^–1
3. \(28\) ms^–1
4. \(10\) ms^–1

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, in case (a) and case (b), respectively: