Perfectly Inelastic Collision

Q. Underline the correct alternative : (a) When a conservative force does positive work on a body, the potential energy of the body increases/decreases/remains unaltered. (b) Work done by a body against friction always results in a loss of its kinetic/potential energy. (c) The rate of change of total momentum of a many-particle system is proportional to the external force/sum of the internal forces on the system. (d) In an inelastic collision of two bodies, the quantities which do not change after the collision are the total kinetic energy/total linear momentum/total energy of the system of two bodies.

Q.

A body of mass 2 kg moving with a velocity of 3 m/sec collides head on with a body of mass 1 kg moving in opposite direction with a velocity of 4 m/sec. After collision, two bodies stick together and move with a common velocity which in m/sec is equal to

1. 1/4

2. 1/3

3. 2/3

4. 3/4

Q.

A body of mass 5 kg explodes at rest into three fragments with masses in the ratio 1 : 1 : 3. The fragments with equal masses fly in mutually perpendicular directions with speeds of 21 m/s. The velocity of the heaviest fragment will be

1. 11.5 m/s

2. 14.0 m/s

3. 7.0 m/s

4. 9.89 m/s

Q.

If the momentum of a body increases by 0.01%, its kinetic energy will increase by

1. 0.01%

2. 0.02%

3. 0.04%

4. 0.08%

Q.

The coefficient of restitution e for a perfectly inelastic collision is

1. 1

2. 0

3. 

4. - 1

Q. A body of mass m moving with a speed v suffers an inelastic collision with another body of M at rest and sticks to it, the ratio of the final kinetic energy of the system to the initial kinetic energy is

1. 
2. 
3. 
4. 

Q.

A body of mass m moving with a constant velocity v hits another body of the same mass moving with the same velocity v but in the opposite direction and sticks to it. The velocity of the compound body after collision is

1. 2v

2. Zero

3. v

4. v/2

Q.

A block of mass 5 kg is on a rough horizontal surface and is at rest. Now a force of 24 N is imparted to it with negligible impulse. If the coefficient of kinetic friction is 0.4 and g=9.8 $m/s^2$, then the acceleration of the block is

1. 0.39 m/s2

2. 0.26 m/s2

3. 0.69 m/s2

4. 0.88 m/s2

Q.

A body of mass $m_1$ is moving with a velocity 'v'. It collides with another stationary body of mass $m_2$. They get embedded. At the point of collision, the velocity of the system is

1. Increases

2. Decreases but does not become zero

3. Remains same

4. Become zero

Q. Two particles A and B move with cons†an t velocities v1 and v2 .At the initial moment their position vectors are r1 and r2 respectively.Find the condition for which particles A and B collides\{Re-Aipmt 2015

Q. A ball of mass m moving horizontally at a speed v collides with the bob of a simple pendulum at rest. The mass of the bob is also m. If the collision is perfectly inelastic, the height to which the two balls
rise after the collision will be given by

1. 
2. 
3. 
4. 

Q.

A particle of mass m moving eastward with a speed v collides with another particle of the same mass moving northward with the same speed v. The two particles coalesce on collision. The new particle of mass 2m will move in the north-easterly direction with a velocity

1. v/2

2. 2v

3. 

4. v

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 bag (mass M) hangs by a long thread and a bullet (mass m) comes horizontally with velocity v and gets caught in the bag. Then for the combined (bag + bullet) system

1. 

2. 

3. 

4. 

Q.

A moving body of mass m and velocity 3 km/h collides with a body at rest of mass 2m and sticks to it. Now the combined mass starts to move. What will be the combined velocity

1. 3 km/h

2. 2 km/h

3. 1 km/h

4. 4 km/h

Q. A disc rotating about its axis with angular speed ${\omega }_o$ is placed lightly (without any translational push) on a perfectly frictionless table. The radius of the disc is R. What are the linear velocities of the points A, B and C on the disc shown in Fig.?

Q.

State the SI unit of momentum?

Q. Q ​A mass m moves with a velocity v and collides inelastically with another identical mass at rest.
After collision the first mass moves with velocity $\frac{v}{\sqrt{3}}$ in a direction perpendicular to the initial direction
of motion. Find the speed of the second mass after collision :$$\begin{gathered} 1.\frac{2v}{\sqrt{3}} \\ 2.\frac{{\displaystyle v}}{{\displaystyle \sqrt{3}}} \\ 3.v\sqrt{\frac{2}{3}} \\ 4.Thesituationoftheproblemisnotpossiblewithoutexternalimpulse \end{gathered}$$

Q.

A body of mass 'm' moving with a constant velocity 'v' hits another body of the same mass moving with the same velocity 'v' but in the opposite direction and sticks to it. The velocity of the compound body after collision is

1. v

2. 2v

3. Zero

4. $\frac{v}{2}$

Q. A bullet of mass $10g$ and speed $500m/s$ is fired into a door and gets embedded exactly at the center of the door. The door is $1.0m$ wide and weighs $12kg$. It is hinged at one end and rotates about a vertical axis practically without friction. Find the angular speed of the door just after the bullet embeds into it.

Q. Consider the situation shown in the figure (8-E2). The system is released from rest and the block of mass 1kg is found to have a speed 0⋅3 m/s after it has descended a distance of 1 m. Find the coefficient of kinetic friction between the block and the table.
Figure

Q.

A bullet of mass a and velocity b is fired into a large block of mass c. The final velocity of the system is

1. $\frac{c}{a+b}.b$

2. $\frac{a}{a+c}.b$

3. $\frac{a+b}{c}.a$

4. $\frac{a+c}{a}.b$

Q. A particle of mass $m$ moving in the $x-$ direction with speed $2v$ is hit by another particle of mass $2m$ moving in the $y-$ direction with speed $v$. If the collision is perfectly inelastic, then loss in energy$\left(\%\right)$ during the collision is close to

1. $40\%$
2. $50\%$
3. $56\%$
4. $62\%$

Q. Two balls having masses m and 2m are fastened to two light strings of same length l. The other ends of the strings are fixed at O. The strings are kept in the same horizontal line and the system is released from rest. The collision between the balls is elastic. (a) Find the velocity of the balls just after their collision. (b) How high will the ball rise after the collision?
Figure

Q. A ball hits a floor and rebounds after an inelastic collision. In this case
(a) the momentum of the ball just after the collision is same as that just before the collision
(b) the mechanical energy of the ball remains the same during the collision
(c) the total momentum of the ball and the earth is conserved
(d) the total energy of the ball and the earth remains the same

Q.

ILLUSTRATION: A particle (a mud pallet, say)of mass m strikes a smooth stationary wedge of mass $M$

with a velocity $v_0$, at an angle $\theta$ with horizontal. If the collision is perfectly inelastic, find the velocity of

the wedge just after the collision.

1. 

2. 

3. 

4. 

Q. Prove the result that the velocity v of translation of a rolling body (like a ring, disc, cylinder or sphere) at the bottom of an inclined plane of a height h is given by
$v^2=\frac{2gh}{\frac{1+k^2}{R^2}}$
using dynamical consideration (i.e. by consideration of forces and torques). Note k is the radius of gyration of the body about its symmetry axis, and R is the radius of the body. The body starts from rest at the top of the plane.

Q. a car of mass 1000 kg rests on a horizontal road initially. it is then pushed over a distance of 5 m to a speed of 1 m/s before the engine is started. if the average frictional force acting on the car is 500 N, the total work done in moving the car before the driver starts the engine?

Q. A box of mass $2\text{kg}$ slides from a height of $8\text{m}$ on the inclined plane and struck the ball. After collision, the ball sticks on the box. If mass of the ball is $200\text{g}$, then what will be the velocity of the box after collision? Assuming all surfaces are frictionless and initially the ball is at rest. (take $g=10m/s^2)$

1. $2.3\text{m/s}$
2. $4.5\text{m/s}$
3. $8.5\text{m/s}$
4. $11.5\text{m/s}$