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

When a spring is subjected to 4 N force, its length is a metre and if 5 N is applied, its length is b metre. If 9 N is applied, its length will be:

1.  4b – 3a

2.  5b – a

3.  5b – 4a

4.  5b – 2a

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

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. \(25U\)

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.  \(0.15~\text{m}\)