A block of mass \(m\) is moving with initial velocity \(u\) towards a stationary spring of stiffness constant \(k\) attached to the wall as shown in the figure. Maximum compression of the spring is:
(The friction between the block and the surface is negligible).
                 

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:

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. \(mg(h-d)+\frac{1}{2}kd^2\)

The potential energy of a long spring when stretched by \(2\) cm is \(U\). If the spring is stretched by \(8\) cm, the potential energy stored in it is:
1. \(4U\)
2. \(8U\)
3. \(16U\)
4. \(U/4\)

A mass of \(0.5~\text{kg}\) moving with a speed of \(1.5~\text{m/s}\) on a horizontal smooth surface, collides with a nearly weightless spring with force constant \(k=50~\text{N/m}.\) The maximum compression of the spring would be:
                   
1.  \(0.12~\text{m}\) 
2.  \(1.5~\text{m}\) 
3.  \(0.5~\text{m}\) 
4.  \(0.15~\text{m}\) 

When a long spring is stretched by \(2\) cm, its potential energy is \(U\). If the spring is stretched by \(10\) cm, the potential energy stored in it will be:
1. \(U/5\)
2. \(5U\)
3. \(10U\)
4. \(25U\)

Two springs A and B having spring constant $K_A$ $and$ $K_B$ $$ $(K_A$ $=$ $2K_B)$ are stretched by applying a force of equal magnitude. If the energy stored in spring A is E, then the energy stored in B will be:

1.  2E

2.  $\frac{E}{4}$

3. $\frac{E}{2}$

4.  4E

If two springs, A and B $(K_A$ $=$ $2$ $K_B),$ are stretched by the same suspended weights, then the ratio of work done in stretching is equal to:
1.  1 : 2
2.  2 : 1
3.  1 : 1
4.  1 : 4