Partially Inelastic Collision

Q.

A ball is thrown vertically downwards from a height of 20m with an initial velocity $v_0$. It collides with the ground, loses 50 percent of its energy in collision and rebounds to the same height. The initial velocity $v_0$ is:

1. 10 m/s

2. 28 m/s

3. 14 m/s

4. 20 m/s

Q.

A trolley filled with sand moves on a smooth horizontal surface with a velocity V0 . A small hole is made at the base of it from which sand is leaving out vertically down at constant rate. As the sand leaves out

As the sand leaves out

a. the velocity of the trolley remains constant

b. the velocity of the trolley increases

c. the velocity of the trolley decreases

d. the momentumof trolley + leakedout sand is conserved

1. a & b are correct

2. c & d are correct

3. a & c are correct

4. b & d are correct

Q. A 100 g ball moving with a velocity of 20 m/s returns in opposite direction with a velocity of 30 m/s after striking a bat. Find the impulse.

Q.

A metal ball of mass $2kg$ moving with a velocity of $36km/h$ has a head on collision with a stationary ball of mass $3kg$. If after the collision, the two balls move together, the loss in kinetic energy due to collision is

1. $40J$

2. $60J$

3. $100J$

4. $140J$

Q. A $25\times {10}^{-3}{\text{m}}^3$ volume cylinder is filled with $1$ mol of $O_2$ gas at room temperature $\left(300\text{K}\right)$. The molecular diameter of $O_2$, and its root mean square speed, are found to be $0.3\text{nm}$ and $200\text{m/s}$, respectively. what is the average collision rate (per second) for an $O_2$ molecule ?

1. $\sim {10}^{11}$
2. $\sim {10}^{12}$
3. $\sim {10}^{13}$
4. $\sim {10}^{10}$

Q.

A thin rod of mass $ 0.9 kg$ and length $ 1 m$ is suspended, at rest, from one end so that it can freely oscillate in the vertical plane. A particle of mass $ 0.1 kg$ moving in a straight line with a velocity of $ 80 \raisebox{1ex}{$m$}\!\left/ \!\raisebox{-1ex}{$s$}\right.$ hits the rod at its bottommost point and sticks to it (see figure). The angular speed $ \left(in \raisebox{1ex}{$rad$}\!\left/ \!\raisebox{-1ex}{$s$}\right.\right)$ of the rod immediately after the collision will be __________.

If

Q. A ball hits the floor and rebounds after an inelastic collision. In this case,

1. The momentum of the ball just after the collision is same as that just before the collision.
2. The total momentum of the ball and the earth is conserved.
3. The kinetic energy of the ball remains the same during the collision.
4. None of the above

Q. A particle strikes a horizontal smooth floor with a velocity $u$ making an angle $\theta$ with the floor and rebounds with velocity $v$ making an angle $\varphi$ with the floor. If the coefficient of restitution between the particle and the floor is $e$, then

1. the impulse delivered by the floor to the body is $mu(1+e)\sin \theta$.
2. $\tan \varphi =e\tan \theta$
3. $v=u\sqrt{1-(1-e^2){\sin }^2\theta }$
4. The ratio of the final kinetic energy to the initial kinetic energy is $({\cos }^2\theta +e^2\sin \theta )$

Q. A metal ball falls from a height of $1\text{m}$ on a steel plate and jumps upto a height of $81\text{cm}$. Find the coefficient of restitution for the collision.

1. $0.7$
2. $0.8$
3. $0.6$
4. $0.9$

Q. Collision frequency of a nitrogen molecule in a cylinder containing nitrogen at $2\text{atm}$ and temperature of ${17}^{\circ }\text{C}$
(Assume radius of a nitrogen molecule to be $1.0\stackrel{\circ }{\text{A}}$)

1. $6\times {10}^9{\text{s}}^{-1}$
2. $8\times {10}^9{\text{s}}^{-1}$
3. $4.6\times {10}^9{\text{s}}^{-1}$
4. $7\times {10}^9{\text{s}}^{-1}$

Q.

What happens to the momentum of a body when velocity is doubled and mass gets halved.

Q. Distinguish between elastic and inelastic collision.

Q. Particles P and Q of mass 20 g and 40 g respectively are simultaneously projected from points A and B on the ground. The initial velocities of P and Q makes ${45}^{\circ }$ and ${135}^{\circ }$ angles respectively with the horizontal AB as shown in the figure. Each particle has an initial speed of 49 m/s. The separation AB is 245 m. Both particle travel in the same vertical plane and undergo a collision. After the collision, P retraces its path. How much time after the collision does the particle Q take to reach the ground? Take $g=9.8m/s^2$

1. 3.5 s
2. 4.5 s
3. 5.5 s
4. 2.5 s

Q. A ball is moving with a speed of $4\text{m/s}$ towards a heavy wall. The wall is also moving towards the ball with velocity of $1\text{m/s}$. If the coefficient of restitution is $0.5$, find the velocity of the ball immediately after the collision. (Assume that the wall maintains the same speed even after the collision.)

1. $3.5\text{m/s}$ along initial direction.
2. $1.5\text{m/s}$ opposite to initial direction.
3. $2.5\text{m/s}$ opposite to initial direction.
4. $3.5\text{m/s}$ opposite to initial direction.

Q.

Two small balls of masses ${}^{\prime }{m}^{\prime }$ and ${}^{\prime }2m^{\prime }$ are placed in a fixed smooth horizontal circular hollow tube of mean radius ${}^{\prime }{r}^{\prime }$ as shown. The ball of mass ${}^{\prime }{m}^{\prime }$ is moving with speed ${}^{\prime }{u}^{\prime }$ and the ball of mass ${}^{\prime }2m^{\prime }$ is stationary. After their first collision, the time elapsed for next collision is: (coefficient of restitution $e$ = $\frac{1}{2}$)

1. 

2. 

3. 

4. 

Q.

A 50 kg skater is travelling due east at a speed of $9m/s$. Another 70 kg skater is moving due south at a speed of $7m/s$. They collide and hold on to each other after the collision. Determine the magnitude and direction of their combined velocity after collision.

Q.

Velocity and acceleration vectors of a charged particle moving perpendicular to the direction of a magnetic field at a given instant of time are $v=2i+Cj$ and $a=3i+4j$ respectively. What is the value of C?

Q.

A body is coming down an inclined plane with an acceleration of 1 m/s². If it starts from rest, find the time after which its velocity becomes 5 m/s.

Q. Which of the following statements is incorrect regarding a partially inelastic collision?

1. Impulse of reformation is equal to the impulse of deformation.
2. Momentum remains conserved if other external forces are absent on the colliding object.
3. Total mechanical energy is not conserved during inelastic collision.
4. Coefficient of restitution lies in the range $(0<e<1)$

Q. A bead of mass $\frac{1}{2}\text{kg}$ starts from rest from point $\text{A}$ and moves in a vertical plane along a smooth fixed quarter ring of radius $5\text{m}$, under the action of a constant horizontal force $F=5\text{N}$ as shown in the figure. The speed of the bead as it reaches the point $\text{B}$ is (Take $g=10{\text{m/s}}^2)$

1. $14.14\text{m/s}$
   
2. $7.07\text{m/s}$
3. $5\text{m/s}$
4. $25\text{m/s}$

Q.

A particle of mass 100 g moving at an initial speed u collides with another particle of same mass kept initially at rest. If the total kinetic energy becomes 0.2 J after the collision, what could be the maximum and the minimum value of u.

Q.

A ball of mass ${}^{\prime }{m}^{\prime }$ moving horizontally which velocity ${}^{\prime }{u}^{\prime }$ hits a wedge of mass ${}^{\prime }{M}^{\prime }$. the wedge is situated on a smooth horizontal surface. If after striking wedge the ball starts moving in vertical direction and the wedge starts moving in horizontal plane. Calculate the coefficient of restitution $e$.

1. 

2. 

3. 

4. 

Q. In the figure shown, a block $A$ moving with velocity $20\text{m/s}$ on a horizontal surface collides with another identical block $B$, initially at rest. The coefficient of restitution is $0.5$. Neglect friction everywhere. The distance between the blocks, $5\text{sec}$ after the collision takes place is

1. $50\text{m}$
2. $125\text{m}$
3. $100\text{m}$
4. $150\text{m}$

Q. A metal ball is moving with velocity $10\text{m/s}$ in downward direction as shown in the figure. After collision with a surface having coefficient of restitution $\left(e\right)=0.6$, it rebounds back. Find the rebound velocity. (Assume the surface remains stationary)

1. $10\text{m/s}$
2. $6\text{m/s}$
3. $60\text{m/s}$
4. $0.06\text{m/s}$

Q.

A particle of mass m moving towards west with a speed v collides with another particle of mass m moving towards south. If two particles stick to each other the speed of the new particle of mass 2m will be?

Q.

A car moving with an initial velocity of $60m/s$ is brought to rest in $30s$. Calculate the acceleration?

Q.

Two bodies of same mass are moving with velocities v and 3v, respectively. Compare their momentum.

Q. A body P strikes head-on with another body Q of mass that is 'p' times that of body P and moving with a velocity that is $\frac{1}{q}$ of the velocity of body P. If the body P comes to rest, the coefficient of restitution is

1. 
2. 
3. 
4. 

Q. In a $1\text{D}$ motion, ball $B$ is ahead of $A$. Ball $A$ is moving with a speed of $10\text{m/s}$ towards $B$ and ball $B$ is moving with speed $15\text{m/s}$ towards ball $A$. After the collision, ball $A$ starts moving with a speed of $5\text{m/s}$ towards ball $B$ and ball $B$ starts moving with a speed of $20\text{m/s}$ away from $A$. Find the coefficient of restitution $\left(e\right)$.

1. $0.3$
2. $0.4$
3. $0.8$
4. $0.6$

Q.

A sphere of mass m moving with a constant velocity u hits another stationary sphere of the same mass. If e is the coefficient of restitution, then the ratio of the velocity of two spheres after collision will be

1. 

2. 

3. 

4.