A bullet of mass m and velocity \(\text v\) is fired into a block of mass \(M\) and sticks to it. The final velocity of the system equals
1. \(\frac{\text{M}}{\text{~m}+\text{M}} \cdot \text{v}\)
2. \(\frac{\text{~m}}{\text{~m}+\text{M}} \cdot \text{v}\)
3. \(\frac{\text{~m}+\text{M}}{m} \cdot \text{v}\)
4. None of these

A particle P moving with speed v undergoes a head-on elastic collision with another particle Q of identical mass but at rest.  After the collision-

1. both P and Q move forward with speed $\frac{v}{2}$.

2. both P and Q move forward with speed $\frac{v}{\sqrt{2}}$.

3. P comes to rest and Q moves forward with speed v.

4. P and Q move in opposite directions with speed $\frac{v}{\sqrt{2}}$.

One projectile moving with velocity v in space, gets burst into 2 parts of masses in the ratio 1:3.  The smaller part becomes stationary.  What is the velocity of the other part?

1. 4v                       

2. v

3. $\frac{4v}{3}$                     

4. $\frac{3v}{4}$

A stationary bomb explodes into two parts of masses 3kg and 1kg. The total KE of the two parts after explosion is 2400 J. The KE of smaller part is 

1. 600 J

2. 1800 J

3. 1200 J

4. 2160 J

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

The relation between velocity (v) and time (t) is $v\propto \sqrt{\mathrm{t}}$, then which one of the following quantity is constant?

1.  Force

2.  Power

3.  Momentum

4.  Kinetic Energy

A force F is applied on a body which moves with a velocity v in the direction of the force, then the power will be

1.  ${\mathrm{Fv}}^2$

2.  Fv

3.  $\mathrm{F}/{\mathrm{v}}^2$

4.  F/v

Three different objects of mass $m_1,$ $m_2$ and m₃ are allowed to fall from rest and from the same point ‘O’ along three different frictionless paths. The speeds of the three objects, on reaching the ground, will be in the ratio of: