COM in Collision and Explosion

Q. Two blocks of masses $m_1$ and $m_2$ connected by a massless spring of spring constant 'k' rest on a smooth horizontal plane as shown in figure. Block 2 is shifted a small distance 'x' to the left and the released. Find the velocity of centre of mass of the system after block 1 breaks off the wall.

1. $\frac{\sqrt{m_{2}K}}{m_1+m_2}$x
2. $\frac{\sqrt{m_{1}K}}{m_1+m_2}$x
3. $\frac{\sqrt{(m_1+m_2)K}}{m_1+m_2}x$
4. zero

Q. A cannon and a supply of cannon balls are inside a sealed rail road car. The cannon fires to the right, and the car recoils to the left. The cannon balls remain in the car after hitting the far wall. Find the maximum distance by which the rail road car move assuming it starts from the rest.

1. $\frac{L}{2}$
2. $L$
3. $0$
4. Can't determine

Q.

A ball of mass 50 g moving at a speed of 2.0 m/s strikes a plane surface at an angle of incidence ${45}^{\circ }$ . The ball is reflected by the plane at equal angle of reflection with the same speed. Calculate (a) the magnitude of the change in momentum of the ball (b) the change in the magnitude of the momentum of the ball.

1. Zero, 0.14 kg m/s

2. 0.14 kg m/s, 0.14 kg m/s

3. 0.14 kg m/s, Zero

4. Zero, Zero

Q. When the speed of an object is doubled, its momentum will be:

1. Halved
2. Same
3. Doubled
4. Quadrupled

Q.

Light in certain cases may be considered as a stream of particles called "photons". Each photon has a linear momentum $\frac{h}{\lambda }$ where h is the Planck's constant and $\lambda$ is the wavelength of the light. A beam of light of wavelength $\lambda$ is incident on a plane mirror at an angle of incidence $\theta$. Calculate the change in the linear momentum of a photon as the beam is reflected by the mirror.

1. $\frac{2h}{\lambda }sin\theta$

2. $\frac{4h}{\lambda }sin\theta$

3. $\frac{4h}{\lambda }cos\theta$

4. $\frac{2h}{\lambda }cos\theta$