Final Velocities

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.

What are deforming force and restoring force?

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 body of mass 1kg is executing SHM given by
X=6cos(100t+π/4)cm
Determine the maximum kinetic energy of the body.

Q.

Two blocks of masses 10 kg and 20 kg moving at speeds of 10 m $s^{-1}$ and 20 m $s^{-1}$ respectively in opposite directions, approach each other and collide. If the collision is completely inelastic, find the thermal energy developed in the process.

Q.

A disc of mass 5kg and radius 50cm rolls on the ground with a velocity of 10m/s . Calculate the kinetic energy of disc ( I= MR²/2)

Q. A solid cylinder of mass 20kg rotate about it's axis with angular speed of 100 rad/s the radius of the cylinder is 0.25 m the kinetic energy associated with the rotation of the cylinder is

Q.

A bomb at rest explodes into two fragments of mass 3 kg and 1 kg The total kinetic energy of fragments is 6×10⁴ J. Calculate kinetic energy of bigger fragment.

Q. Three blocks are initially placed as shown in the figure. Block $A$ has mass $m$ and initial velocity $v$ to the right. Block $B$ with mass $m$ and block $C$ with mass $4m$ are both initially at rest. Neglect friction. All collisions are elastic. The final velocity of block $A$ is

1. $0.6v$ to the left
2. $0.4v$ to the left
3. zero
4. $0.4v$ to the right

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. 1.8 kg
3. 1.2 kg
4. 1.5 kg

Q. A ball is moving with a speed of $5\text{m/s}$ towards a heavy wall which is moving towards the ball with speed $2\text{m/s}$ as shown in figure. Assuming the collision to be perfectly elastic, find the speed of the ball and speed of the wall immediately after the collision.

1. $9\text{m/s},3\text{m/s}$
2. $7\text{m/s},3\text{m/s}$
3. $9\text{m/s},2\text{m/s}$
4. $7\text{m/s},2\text{m/s}$

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. 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.

Consider a gravity-free hall in which an experimenter of mass 50 kg is resting on a 5 kg pillow, 8 ft above the floor of the hall. He pushes the pillow down so that it starts falling at a speed of 8 ft/s. The pillow makes a perfectly elastic collision with the floor, rebounds and reaches the experimenter's head. Find the time elapsed in the process.

1. 2.88 s

2. 1.22 s

3. 2.22 s

4. 0.22 s

Q. Two blocks (mass M and 2 M) are placed on a horizontal frictionless surface connected by an ideal spring. Initially, everything is at rest and there is a string compressing the mass-spring system from equilibrium. At some time after the string is cut, the block of 2M mass reaches its maximum kinetic energy of 20 J. What maximum kinetic energy does the block of mass M attain?

1. 10 J
2. 20 J
3. 40 J
4. 30 J

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. 

2. 

3. 

4. 

Q. Two perfectly elastic particles P and Q of equal mass travel along the line joining them with velocities 15 m/sec and 10 m/sec in opposite direction. After collision, the velocity of P is and that of Q is respectively (in m/sec).

1. \N
2. 5
3. 10
4. 15
5. 20

Q.

Name the force involved in the following cases:

A stretched rubber band regains its original shape.

Q. Two masses $m$ and $2m$ are placed in a fixed horizontal circular smooth hollow tube of radius $r$ as shown. The mass $m$ is moving with speed $u$ and the mass $2m$ is stationary. Then choose the correct option(s). (Coefficient of restitution, $e=\frac{1}{2})$

1. The velocity of the mass $2m$ after collision will be $\frac{2u}{3}$
2. The velocity of the mass $m$ after collision will be $\frac{2u}{3}$
3. Time elapsed for next collision after their first collision will be $\frac{2\pi r}{u}$
4. All the above.

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 collision?

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

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. 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 large body of mass 100 kg moving with a velocity of 10.0 m/s collides elastically with a small body of mass 100 g at rest. The velocity of the small body, after collision, is.

1. 5 m/s
2. 10 m/s
3. 25 m/s
4. 20 m/s

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

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 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. 
2. 
3. 
4. 

Q. Which of the following statement(s) is (are) CORRECT?
1. Gusset plate material is saved by using a lug angle but extra material is required for lug angles and their connection.
2. The load carrying capacity of the tension member will be maximum if gusset plate is in between the two angles and tacking rivets are provided.

1. 1 only
2. 2 only
3. 1 and 2 both
4. None of these

Q.

A sphere collides with another sphere of identical mass. After collision, the two spheres move. The collision is inelastic. Then the angle between the directions of the two spheres is

1. $90°$

2. $0°$

3. $45°$

4. Different from $90°$

Q. Two balls of masses $5\text{kg}$ and $10\text{kg}$ are at the positions shown in figure. The track on which the balls move is frictionless. Initially, the $10\text{kg}$ ball is kept at rest and the $5\text{kg}$ ball is dropped with speed $v$ from height $5\text{m}$. Assuming the collision between the balls is perfectly elastic, find the value of ${}^{\prime }{v}^{\prime }$ such that the $10\text{kg}$ ball reaches point ${}^{\prime }{C}^{\prime }$.

1. $0\text{m/s}$
2. $22.4\text{m/s}$
3. $11.2\text{m/s}$
4. $10\text{m/s}$