Com in Perfectly Inelastic Collision

Q. A neutron of mass $1.67\times {10}^{-27}kg$ is moving with a velocity $1.2\times {10}^{7}m{s}^{-1}$ collides head-on with a deuteron of mass $3.34\times {10}^{-27}kg$ initially at rest. If the collision is perfectly inelastic, the speed of the composite particle will be

1. $2\times {10}^{6}m{s}^{-1}$
2. $4\times {10}^{6}m{s}^{-1}$
3. $6\times {10}^{6}m{s}^{-1}$
4. $8\times {10}^{6}m{s}^{-1}$

Q.

A shell initially at rest explodes into two pieces of equal mass, then the two pieces will

1. Be at rest

2. Move with different velocities in different directions

3. Move with the same velocity in opposite directions

4. Move with the same velocity in same direction

Q. A ball of mass $m$ moving with speed $u$ undergoes a head on collision with a stationary ball of mass $3m$. If collision is perfectly inelastic, find the loss of kinetic energy.

1. $\frac{1}{4}m{u}^2$
2. $\frac{1}{8}m{u}^2$
3. $\frac{1}{16}m{u}^2$
4. $\frac{3}{8}m{u}^2$

Q. A spherical shell at rest at the origin explodes into three fragments of masses 1 kg, 2 kg and 'm' kg. The 1 kg and 2 kg pieces fly off with speeds of $12m{s}^{-1}$ along the x-axis and 8 $m{s}^{-1}$ along the y-axis respectively. If the 'm' kg piece flies off with a speed of 40 $m{s}^{-1}$ , the total mass of the shell must be

1. 3.5 kg
2. 4.0 kg
3. 4.5 kg
4. 5.0 kg

Q. Two identical particles collide in the air in an perfectly inelastic manner. Before collision, one moves horizontally and the other moves in vertical direction with equal speed. After collision, the fractional loss in kinetic energy of the system of particles is

1. $\frac{1}{2}$
2. $\frac{1}{\sqrt{2}}$
3. $\frac{\sqrt{3}}{2}$
4. $0$

Q.

A light and a heavy body, having equal momenta, have equal kinetic energies.

1. True
2. False

Q. A body of mass 5 kg is moving along the x-axis with a velocity 2$m{s}^{-1}$. Another body of mass 10 kg is moving along the y-axis with a velocity $\sqrt{3}m{s}^{-1}$. If they collide at the origin and stick together, then the final velocity of the combined mass is

1. $\sqrt{3}m{s}^{-1}$
2. $(\sqrt{3}+1)m{s}^{-1}$
3. $\frac{4}{3}m{s}^{-1}$
4. $None$

Q. Object $A$ of mass $m$, is moving at a velocity $v_1$ to the right. It collides and sticks to object $B$ of mass $m_2$ moving in the same direction as object $A$ with velocity $v_2$. After collision, both the objects have the same velocity $\frac{1}{2}(v_1+v_2)$. What is the relationship between $m_1$ and $m_2$? [$v_1$ and $v_2$ are not equal]

1. $m_1=m_2$
2. $m_1=2m_2$
3. $m_1=m_2/2$
4. $m_1=4m_2$

Q.

A 2 kg mass moving with a velocity of $10m{s}^{-1}$ collides with another 6 kg mass moving in opposite direction with a velocity of $20m{s}^{-1}$. After the collision, they stick and move together. Find their common velocity and the momentum.

1. $12.5m/s,100kgm{s}^{-1}$

2. $12.5m/s,50kgm{s}^{-1}$

3. $7.5m/s,100kgm{s}^{-1}$

4. $7.5m/s,50kgm{s}^{-1}$

Q.

A wooden block of mass M rests on a horizontal surface. A bullet of mass m moving in the horizontal direction strikes and gets embedded in it. The combined system covers a distance x on the surface. If the coefficient of friction between wood and the surface is $\mu$, the speed of the bullet at the time of striking the block is (where m is mass of the bullet)

1. $\sqrt{\frac{2mg}{\mu m}}$

2. $\sqrt{\frac{2\mu mg}{mx}}$

3. $\sqrt{2\mu gx}\left(\frac{M+m}{m}\right)$

4. $\sqrt{\frac{2\mu mx}{M+m}}$

Q. A shell of mass '2m' fired with a speed 'u' at an angle $\theta$ to the horizontal explodes at the highest point of its motion into two fragments of mass 'm' each. If one fragment, falls vertically, the distance at which the other fragment falls from the gun is given by

1. $\frac{3}{2}\frac{u^{2}sin2\theta }{g}$
2. $\frac{2u^{2}sin2\theta }{g}$
3. $\frac{u^{2}sin2\theta }{g}$
4. $\frac{3u^{2}sin2\theta }{g}$

Q.

A body of mass 6 kg collides with another body at rest. After the collision, they travel together with a velocity that is one third of the initial velocity of 6 kg mass. The mass of the second body is

1. 60 kg

2. 30 kg

3. 12 kg

4. 18 kg

Q. A shell of mass '2m' fired with a speed 'u' at an angle $\theta$ to the horizontal explodes at the highest point of its motion into two fragments of mass 'm' each. If one fragment, falls vertically, the distance at which the other fragment falls from the gun is given by

1. $\frac{3}{2}\frac{u^{2}sin2\theta }{g}$
2. $\frac{2u^{2}sin2\theta }{g}$
3. $\frac{u^{2}sin2\theta }{g}$
4. $\frac{3u^{2}sin2\theta }{g}$

Q.

A bullet of mass 20g travelling horizontally with a speed of 500 m/s passes through a wooden block of mass 10.0 kg initially at rest on a level surface. The bullet emerges with a speed of 100 m/s and the block slides 20 cm on the surface before coming to rest. The friction coefficient between the block and the surface is $g=10m{s}^{-2}$

1. 0.16

2. 0.24

3. 0.32

4. 0.50