A spring \(40~\text {mm}\) long is stretched by the application of a force. If \(10 ~\text{N}\) force required to stretch the spring through \(1 ~\text{mm,}\) then work done in stretching the spring through \(40 ~\text{mm}\) is

1. \(84~\text{J}\)

2. \(68~\text{J}\)

3. \(23~\text{J}\)

4. \(8~\text{J}\)

Two springs with spring constants $k_1$ = 1500 N/m and $k_2$ = 3000 N/m are stretched by the same force. The ratio of potential energy stored in the springs will be 

1. 2:1

2. 1:2

3. 4:1

4. 1:4

A block of mass 2 kg moving with velocity of 10 m/s on a smooth surface hits a spring of force constant $80\times {10}^3$ N/m as shown. The maximum compression in the spring is

1. 5 cm

2. 10 cm

3. 15 cm

4. 20 cm

A block of mass m = 25 kg on a smooth horizontal surface with a velocity $\overrightarrow{v}$ =3 $m{s}^{-1}$ meets the spring of spring constant k = 100 N/m fixed at one end as shown in the figure. The maximum compression of the spring and velocity of the block as it returns to the original position respectively are: 

1.  1.5 m, -3 $m{s}^{-1}$

2.  1.5 m, 0 $m{s}^{-1}$

3.  1.0 m, 3 $m{s}^{-1}$

4.  0.5 m, 2 $m{s}^{-1}$

A mass m slips along the wall of a semispherical surface of radius R. The velocity at the bottom of the surface is [ MP PMT 1993]

1. $\sqrt{Rg}$

2. $\sqrt{2Rg}$

3. $2\sqrt{\pi Rg}$

4. $\sqrt{\pi Rg}$