Perfectly Elastic Collision

Q.

What are the differences between elastic and inelastic collisions?

Q.

Develop the theory of one-dimensional elastic collision.

Q. Particle $A$ makes a perfectly elastic collision with another particle $B$ at rest. After collision, they fly apart in opposite directions with equal speeds. The ratio of masses $\frac{m_A}{m_B}$ is

1. $1:3$
2. $1:4$
3. $1:2$
4. $1:\sqrt{3}$

Q. Two identical balls marked 2 and 3, in contact with each other and at rest on a horizontal frictionless table, are hit head-on by another identical ball marked 1 moving initially with a speed 'v' as shown in the figure. If the collision is elastic, what is observed?

1. Balls 1 and 2 comes to rest and ball 3 rolls out with speed v.
2. Ball A comes to rest and balls 2 and 3 roll out with speed each.
3. Balls 1, 2 and 3 roll out with speed each.
4. Balls, 1, 2 and 3 come to rest.

Q. A simple pendulum is made of a string of length $l$ and a bob of mass $m$, is released from a small angle ${\theta }_0$. It strikes a block of mass $M$, kept on a horizontal surface at its lowest point of oscillations, elastically. It bounces back and goes up to an angle ${\theta }_1$. Then, $M$ is given by

1. $m\left(\frac{{\theta }_0+{\theta }_1}{{\theta }_0-{\theta }_1}\right)$
2. $m\left(\frac{{\theta }_0-{\theta }_1}{{\theta }_0+{\theta }_1}\right)$
3. $\frac{m}{2}\left(\frac{{\theta }_0-{\theta }_1}{{\theta }_0+{\theta }_1}\right)$
4. $\frac{m}{2}\left(\frac{{\theta }_0+{\theta }_1}{{\theta }_0-{\theta }_1}\right)$

Q.

What is impulsive force?

Q.

Two objects, each of mass $1.5\mathrm{kg}$, are moving in the same straight line but in opposite directions. The velocity of each object is $2.5\mathrm{m}/\mathrm{s}$ before the collision during which they stick together. What will be the velocity of the combined object after collision?

Q. Two identical billiard balls are in contact on a smooth table. A third identical ball strikes them symmetrically and comes to rest after impact. The coefficient of restitution is

1. $\frac{\sqrt{3}}{2}$
2. $\frac{2}{3}$
3. $\frac{1}{3}$
4. $\frac{1}{6}$

Q. Two identical balls A and B having velocities of $0.5m/s$ and $–0.3m/s$ respectively collide elastically in one dimension. The velocities of B and A after the collision respectively will be

1. $–0.3m/s$ and $0.5m/s$
2. $0.3m/s$ and $0.5m/s$
3. $-0.5m/s$ and $0.3m/s$
4. $0.5m/s$ and $-0.3m/s$

Q. A moving particle of mass 'm' makes a head-on collision with a particle of mass '2m' initially at rest. If the collision is perfectly elastic, the percentage loss of energy of the colliding particle is

1. 
2. 
3. 
4. 

Q.

A smooth sphere of mass 'M' moving with velocity 'u' directly collides elastically with another sphere of mass 'm' at rest. After collision their final velocities are 'V' and 'v' respectively. The value of 'v' is

1. 

2. 

3. 

4. 

Q. A particle of mass $m$ describes a circle of radius $r$. The centripetal accelaration of the particle is $\frac{4}{r^2}$.What will be the momentum of the particle?

1. $\frac{4m}{\sqrt{r}}$
2. $\frac{2m}{r}$
3. $\frac{2m}{\sqrt{r}}$
4. None of these

Q. Two particles of masses $m$ and $2m$ moving in opposite direction collides elastically with velocities $2v$ and $v$ respectively. Find their respective magnitude of velocities after the collision.

1. $v,2v$
2. $4v,0$
3. $2v,v$
4. $v,v$

Q. A ball collides with smooth and fixed inclined plane of inclination $\theta$ after falling vertically through a distance $h\text{m}$. If it moves horizontally just after the impact, then the coefficient of restitution is

1. ${\tan }^2\theta$
2. $\cot \theta$
3. ${\cot }^2\theta$
4. $\tan \theta$

Q. A striker is shot from a square carrom board from a point exactly at the mid point of one of the walls with a speed $2\text{m/s}$ at an angle of ${45}^{\circ }$ with the $x-$axis as shown in the figure. The collisions of the striker with the walls of the carrom are perfectly elastic. The coefficient of kinetic friction between the stricker and board is $0.2$. Then,
[Take $g=10{\text{m/s}}^2$]

1. $x-$coordinate of the striker when it stops (taking point $\text{O}$ to be the origin and neglect the friction between wall and striker) is $\frac{1}{2\sqrt{2}}.$
2. $y-$coordinate of the stricker when it stops (taking point $\text{O}$ to be the origin and neglect the friction between wall and striker) is $\frac{1}{2}.$
3. $x-$coordinate of the striker when it stops (taking point $\text{O}$ to be the origin and neglect the friction between wall and striker) is $\frac{1}{\sqrt{2}}.$
4. $y-$coordinate of the stricker when it stops (taking point $\text{O}$ to be the origin and neglect the friction between wall and striker) is $\frac{1}{2\sqrt{2}}.$

Q. A ball is bouncing down a set of stairs. The coefficient of restitution is $e$. The height of each step is $d$ and the ball bounces one step at each bounce. After each bounce the ball rebounds to a height $h$ above the next lower step. Neglect height of each step in comparison to $h$ and assume the impacts to be effectively head on. Which of the following relation is correct? (given that $h>d$)

1. $\frac{h}{d}=1-e^2$
2. $\frac{h}{d}=1-e$
3. $\frac{h}{d}=\frac{1}{1-e^2}$
4. $\frac{h}{d}=\frac{1}{1-e}$

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

1. Total momentum of the system is $3\text{kg m/s}$
2. Momentum of $5\text{kg}$ mass after collision is $4\text{kg m/s}$
3. Kinetic energy of the centre of mass of system is $0.75\text{J}$
4. Kinetic energy of the centre of mass of system is $1.75\text{J}$

Q. A particle of mass $m$ moving with velocity $1\text{m/s}$ collides elastically with another particle of mass $2m$ (initialy at rest). If the incident particle is deflected by ${90}^{\circ }$. The angle $\theta$ made by the heavier mass with the initial direction of motion of mass $m$ will be equal to:
(consider collision to be perfectly elastic)

1. ${15}^{\circ }$
2. ${30}^{\circ }$
3. ${60}^{\circ }$
4. ${45}^{\circ }$

Q.

A block of mass m 2.0 kg moving at $2.0\frac{m}{s}$ collides head on with another block of equal mass kept at rest.(a) Find the maximum possible loss in kinetic energy due to the collision.(b) If the actual loss in kinetic energy is half of this maximum, find the coefficient of restitution.

Q. Two balls $A$ and $B$ having equal masses and moving along the same straight line with velocities $+2\text{m/s}$ and $-5\text{m/s}$ respectively, collide elastically. If rightwards direction is considered as $+vex-$ axis, then their velocities after the collision will be respectively

1. $-5\text{m/s}$ and $+2\text{m/s}$
2. $3\text{m/s}$ for both
3. $5\text{m/s}$ and $1\text{m/s}$
4. None of these

Q.

In an elastic collision of two particles the following is conserved

1. Momentum of each particle

2. Speed of each particle

3. Kinetic energy of each particle

4. Total kinetic energy of both the particles

Q. A wedge of mass $M$ has one face making an angle $\alpha$ with horizontal and is resting on a smooth rigid floor. A particle of mass ${}^{\prime }{m}^{\prime }$ hits the inclined face of the wedge with horizontal velocity $v_0.$ It is observed that the particle rebounds in vertical direction after impact. Calculate the speed of particle after impact.
[Neglect friction between particle and the wedge and take $M=2m,v_0=10\text{m/s},\tan \alpha =2,g=10{\text{m/s}}^2.$]

1. $5\text{m/s}$
2. $0\text{m/s}$
3. $10\text{m/s}$
4. $20\text{m/s}$

Q. A small steel ball $A$ is suspended by an inextensible thread of length $l=1.5\text{m}$ from $O$ as shown in the figure. Another identical ball $B$ is thrown vertically downwards such that its surface remains just in contact with thread during downward motion and collides elastically with the suspended ball. If the suspended ball just complete vertical circle after collision, calculate the Impulse on the steel ball $A$ due to the ball $B$. (Take $g=10{\text{m/s}}^2$ and mass of ball $m=5\text{kg}$)

1. $50\sqrt{2}\text{Ns}$
2. $25\sqrt{3}\text{Ns}$
3. $50\sqrt{3}\text{Ns}$
4. $25\text{Ns}$

Q. A sphere P of mass m and velocity $\overrightarrow{v}$ undergoes an oblique and perfectly elastic collision with an identical sphere Q initially at rest. The angle $\theta$ between the velocities of the spheres after the collision shall be

Q. In a head on elastic collision of a heavy vehicle moving with a velocity of $10{\text{ms}}^{-1}$ and a small stone at rest, the stone will fly away with a velocity equal to

1. $5{\text{ms}}^{-1}$
2. $10{\text{ms}}^{-1}$
3. $20{\text{ms}}^{-1}$
4. $40{\text{ms}}^{-1}$

Q. A ball of mass $m$ strikes the fixed inclined plane after falling through a height $h$. If it rebounds elastically, the impulse imparted on the ball is

1. $2m\sqrt{2gh}\cos \theta$
2. $2m\sqrt{gh}\cos \theta$
3. $2m\sqrt{2gh}\sin \theta$
4. $2m\sqrt{2gh}$

Q. A tunnel is dug inside the earth across one of its diameters. Radius of earth is $R$ and its mass is $M$. A particle is projected inside the tunnel with velocity $\sqrt{\frac{2GM}{R}}$ from one of its ends then maximum velocity attained by the particle in the subsequent motion is (assuming tunnel to be frictionless)

1. $\sqrt{\frac{GM}{R}}$
2. $\sqrt{\frac{3GM}{R}}$
3. $\sqrt{\frac{2GM}{R}}$
4. $\sqrt{\frac{5GM}{R}}$

Q. A gramophone record of mass $M$ and radius $R$ is rotating with angular speed $\omega$. If two pieces of wax each of mass $m$ are kept on it at a distance $\frac{R}{2}$ from the centre on opposite sides, then the new angular velocity will be

1. $\frac{m\omega }{m+M}$
2. $\frac{M\omega }{m+M}$
3. $\frac{M+m}{M\omega }$
4. $\frac{\omega }{2}$

Q. A ball moving with a velocity $v$ hits a massive wall moving towards the ball with a velocity $u$. An elastic impact lasts for time $\Delta t$.

1. The average elastic force acting on the ball is $\frac{\left[m\right(u+v\left)\right]}{\Delta t}.$
2. The average elastic force acting on the ball is $\frac{\left[2m\right(u+v\left)\right]}{\Delta t}.$ ​​​​
3. The kinetic energy of the ball increases by 2mu (u + v)
4. The kinetic energy of the ball remains the same after the collision.

Q.

A bullet of mass 10 g moving horizontally at a speed of $50\sqrt{7}ms/$ strikes a block of mass 490 g kept on a frictionless track as shown in figure (9-E17). the bullet remains inside the block and the system proceeds towards the semicircular track of radius 0.2 m. Where will the block strike the horizontal part after leaving the semicircular track ?