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

A stationary particle explodes into two particles of masses m₁ and m₂ which move in opposite directions with velocities v₁ and v₂. The ratio of their kinetic energies E₁/E2 is:

1. m₂/m₁

2. m₁/m₂

3. 1

4. m₁v₂/m₂v₁

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. \(25U\)

\(250\) N force is required to raise \(75\) kg mass from a pulley. If the rope is pulled \(12\) m, then the load is lifted to \(3\) m. The efficiency of the pulley system will be: 
1. \(25\text{%}\)
2. \(33.3\text{%}\)
3. \(75\text{%}\)
4. \(90\text{%}\)

A child is sitting on a swing. Its minimum and maximum heights from the ground are \(0.75\) m and \(2\) m, respectively. Its maximum speed will be: (Take \(g=10\) m/s²)
1. \(10\) m/s
2. \(5\) m/s
3. \(8\) m/s
4. \(15\) m/s

If the kinetic energy of a body is increased by \(300\)%, then the percentage change in momentum will be:
1. \(100\)%
2. \(150\)%
3. \(265\)%
4. \(73.2\)%

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

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

A particle projected with velocity 'u' makes an angle θ with respect to horizontal. Now it breaks in two identical parts at highest point of trajectory. If one part retraces its path, then velocity of the other part is:
1. 3u cos θ
2. 2u cos θ
3. u cos θ
4. u

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