Final Velocities

Q.

Two particles have masses of $m$ and $4m$ and their kinetic energies are in the ratio of $2:1$. What is the ratio of their linear momenta?

1. $\frac{1}{2}$

2. $\frac{1}{\sqrt{2}}$

3. $\frac{1}{4}$

4. None of these

Q. Two particles of masses $m_1$ & $m_2$ and velocities $u_1$ and $\left(\alpha u_1\right)(\alpha \ne 0)$ make an elastic head on collision. If the initial kinetic energies of the two particles are equal and $m_1$ comes to rest after collision, then

1. $\frac{m_2}{m_1}=9+2\sqrt{2}$
2. $\frac{m_2}{m_1}=3-2\sqrt{2}$
3. $\frac{m_1}{m_2}=3-2\sqrt{2}$
4. $\frac{m_1}{m_2}=9+\sqrt{2}$

Q. A mass $m_1$ moving with initial velocity $u$ strikes head on to another mass $m_2$ kept at rest as shown in figure. After collision if $|v_1|<|u|$, then

1. $m_1>m_2$
2. $m_1<m_2$
3. $m_1=m_2$
4. There is no relation between $m_1$ and $m_2$

Q. Block $A$ with a kinetic energy of $500\text{J}$ collides with another block $B$ of mass $10\text{kg}$ initially kept at rest. Assuming that the collision is perfectly elastic, what is the final speed of the block $B$?

1. $100\text{m/s}$
2. $0\text{m/s}$
3. $10\text{m/s}$
4. $5\text{m/s}$

Q. A point mass of $1\text{kg}$ collides elastically with a stationary point mass of $5\text{kg}$. After their collision, the $1\text{kg}$ mass reverses its direction and moves with a speed of $2\text{m/s}$. Which of the following statements is (are) correct for the system of two masses ?

1. Total momentum of the system is $7{\text{kg ms}}^{-1}$.
2. Momentum of $5\text{kg}$ mass after collision is $5{\text{kg ms}}^{-1}$.
3. Velocity of $5\text{kg}$ after collision is $1\text{m/s}$.
4. Velocity of $1\text{kg}$ before collision is $2\text{m/s}$.

Q. A ball of mass $1\text{kg}$ is thrown with a velocity of $6\text{m/s}$ at a stone of unknown mass initially at rest. If the velocity of the stone after the elastic collision with the ball is $1.5\text{m/s}$, what is the mass of the stone?

1. $8\text{kg}$
2. $5\text{kg}$
3. $7\text{kg}$
4. $10\text{kg}$

Q. A heavy steel ball of mass greater than 1 kg moving with a speed of 2 $mse{c}^{-1}$collides head on with a stationary ping-pong ball of mass less than 0.1 gm. The collision is elastic. After the collision the ping-pong ball moves approximately with speed of.

1. 2 m/s
2. 4 m/s
3. $2\times {10}^4$m/s
4. $2\times {10}^3$m/s

Q. On a frictionless surface, a block of mass $M$ moving at speed $\upsilon$ collides elastically with another block of same mass $M$ which is initially at rest. After collision the first block moves at an angle $\theta$ to its initial direction and has a speed $\frac{\upsilon }{3}$. The second block's speed after the collision is

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

Q. There are $100$ identical blocks equally spaced on a frictionless track as shown in the figure. Initially all the blocks are at rest. Block $\left(1\right)$ is pushed with velocity $v$ towards block $2$. If each of the collisions is elastic, then the velocity of the final ${100}^{th}$ block is

1. $\frac{v}{99}$
2. $\frac{v}{100}$
3. $v$
4. zero

Q. A rifle man, who together with his rifle has a mass of $100\text{kg}$, stands on a smooth surface and fires $10$ shots horizontally. Each bullet has a mass $10\text{g}$ and a muzzle velocity of $800\text{m/s}$. What velocity does the rifle man acquire at the end of $10$ shots?

1. $0.8\text{m/s}$
2. $0.5\text{m/s}$
3. $0.3\text{m/s}$
4. $1.2\text{m/s}$

Q.

A body of mass 1 kg makes an elastic collision with another body at rest and continues to move in the original direction after collision with a velocity equal to $\frac{1}{4}$ of its original velocity. The mass of the second body is

1. $\frac{2}{5}kg$

2. $\frac{3}{5}kg$

3. $\frac{3}{2}kg$

4. $\frac{2}{3}kg$

Q. Balls of masses $4\text{kg}$ and $10\text{kg}$ are moving towards each other with speeds $6\text{m/s}$ and $3\text{m/s}$ respectively on a frictionless surface. After collision, the $4\text{kg}$ ball is observed to return back (towards left) with speed $2\text{m/s}$. Find the velocity of $10\text{kg}$ ball after collision.

1. $2\text{m/s}$
2. $0.2\text{m/s}$
3. $9\text{m/s}$
4. $1\text{m/s}$

Q. A ball P of mass 2 kg undergoes an elastic collision with another ball Q initially kept at rest. After the collision, ball P continues to move in its original direction with a speed one-fourth of its original speed. What is the mass of ball Q?

1. 0.9 kg
2. 1.2 kg
3. 1.5 kg
4. 1.8 kg

Q. Ball $A$ of mass $10\text{kg}$ moving with a velocity $6\text{m/s}$, collides with ball $B$ of mass $50\text{kg}$ which is at rest. What is the ratio of the kinetic energies of the ball $A$ before and after the elastic collision?

1. $9:4$
2. $4:9$
3. $2:3$
4. $3:2$

Q. A body of mass $m_1$ moving at a constant speed undergoes an elastic collision with a body of mass $m_2$ initially at rest., the ratio of the kinetic energies of masses $m_2$ and $m_1$ after the collision is

1. $\frac{m_1{m}_2}{(m_1-m_2{)}^2}$
2. $\frac{\sqrt{2}{m}_1{m}_2}{(m_1-m_2{)}^2}$
3. $\frac{2m_1{m}_2}{(m_1-m_2{)}^2}$
4. $\frac{4m_1{m}_2}{(m_1-m_2{)}^2}$

Q. Two spheres are placed in a horizontal plane with kinetic energies $(KE{)}_A=8\text{J}$ and $(KE{)}_B=18\text{J}$ as shown in figure. If both the spheres collide elastically, find the speed of both the spheres after collision. Both the spheres have the same mass $m=1\text{kg}$.

1. $V_A=6\text{m/s}{V}_B=4\text{m/s}$
2. $V_A=4\text{m/s}{V}_B=6\text{m/s}$
3. $V_A=3\text{m/s}{V}_B=2\text{m/s}$
4. $V_A=2\text{m/s}{V}_B=3\text{m/s}$

Q. Three objects $A$, $B$ and $C$ are kept in a straight line on a frictionless horizontal surface. These have masses $m$, $2m$ and $m$ respectively. The object $A$ moves towards $B$ with a speed of $9\text{m/s}$ and makes an elastic collision with it. Thereafter, $B$ makes completely inelastic collision with $C$. All motions occur on the same straight line. Find the final speed (in m/s) of object $C$.

Q. Two spheres are placed in a horizontal plane with kinetic energies $(KE{)}_A=8\text{J}$ and $(KE{)}_B=18\text{J}$ as shown in figure. If both the spheres collide elastically, find the speed of both the spheres after collision. Both the spheres have the same mass $m=1\text{kg}$.

1. $V_A=6\text{m/s}{V}_B=4\text{m/s}$
2. $V_A=4\text{m/s}{V}_B=6\text{m/s}$
3. $V_A=3\text{m/s}{V}_B=2\text{m/s}$
4. $V_A=2\text{m/s}{V}_B=3\text{m/s}$

Q. $n$ elastic balls are placed at rest on a smooth horizontal plane which is circular at the ends with radius $r$ as shown in the figure. The masses of the balls are $m,\frac{m}{2},\frac{m}{2^2},...,\frac{m}{2^{n-1}}$ respectively. What is the minimum velocity which should be imparted to the first ball of mass $m$ such that this $n^{th}$ ball will complete the vertical circle ?

1. ${\left(\frac{3}{4}\right)}^{n-1}\sqrt{5gr}$
2. ${\left(\frac{4}{3}\right)}^{n-1}\sqrt{5gr}$
3. ${\left(\frac{3}{2}\right)}^{n-1}\sqrt{5gr}$
4. ${\left(\frac{2}{3}\right)}^{n-1}\sqrt{5gr}$

Q. Two balls marked 1 and 2 of the same mass m and a third ball marked 3 of mass M are arranged over a smooth horizontal surface as shown in Fig. Ball 1 moves with a velocity $v{­}_1$ towards balls 2 and 3. All collisions are assumed to be elastic. If M <m, the number of collisions between the balls will be

1. One
2. Two
3. Three
4. Four