Collision Example II

Q.

A ball of mass m moving at a speed v makes a head-on collision with an identical ball at rest. The kinetic energy of the ball after the collision is three-fourths of the original. Find the coefficient of restitution.

Q. A ball of mass $100\text{g}$ and another ball of mass $120\text{g}$ moves towards each other with speeds $6\text{m/s}$ and $5\text{m/s}$ respectively. If they stick to each other after colliding, what would be the velocity of the combined mass after the collision?

1. $0\text{m/s}$
2. $2\text{m/s}$
3. $4\text{m/s}$
4. $6\text{m/s}$

Q.

A ball is projected vertically upward with a speed of 50 m/s. Find

(a) The maximum height,

(b) The time to reach the maximum beight,

(c) The speed at half the maximum geight. take g = $10m/s^2$

Q.

A small particle of mass $m$ moving inside a heavy, hollow and straight tube along the tube axis undergoes elastic collision at two ends. The tube has no friction and it is closed at one end by a flat surface while the other end is fitted with a heavy movable flat piston as shown in figure. When the distance of the piston from closed end is $L=L_o$ the particle speed is $v=v_0$. The piston is moved inward at a very low speed $V$ such that $V<<\frac{dL}{L}{v}_0$
, where $dL$ is the infinitesimal displacement of the piston.




Which of the following statement (s) is/are correct?

1. After each collision with the piston, the particle speed increases by $2V.$

2. If the piston moves inward by dL, the particle speed increases by $2V\frac{dL}{L}$

3. The particle's kinetic energy increases by a factor of 4 when the piston is moved inward from $L_0$ to $\frac{L_0}{2}$

4. The rate at which the particle strikes the piston is $v/L$

Q.

A truck of mass $500kg$ moving at $4m{s}^{-1}$ collides with another truck of mass $1500kg$ moving in the same direction at $2m{s}^{-1}$.What is their common velocity just after the collision if they move off together?

Q. A ball of mass m is dropped onto a floor from a certain height. The collision is perfectly elastic and the ball rebounds to the same height and again falls. Find the average force exerted by the ball on the floor during a long time interval.

1. mg
2. 2mg
3. 0
4. 2.5mg

Q. A light particle moving horizontally with speed 8 m/s hits a very heavy block moving in the same direction with speed 4 m/s, after collision, the speed of particle is 2 m/s along the same direction, then the collision is

1. elastic
2. oblique inelastic
3. inelastic
4. perfectly inelastic

Q.

A ball of mass m is dropped onto a floor from a certain height.The collision is perfectly elastic and the ball rebounds to the same height and again falls.Find the average force exerted by the ball on the floor during a long time interval.

Q.

A $0.5kg$ ball moving with a speed of $12m{s}^{-1}$ strikes a hard wall at an angle of $30°$ with the wall. It is reflected with the same speed and at the same angle. If the ball is in contact with the wall for $0.25s$ the average force acting on the wall is

1. $96N$

2. $48N$

3. $24N$

4. $12N$

Q. A ball of mass 0.50kg moving at a speed of 5.0 m/s collides with another ball of mass 1.0kg. After the collision the balls stick together and remain motionless. Waht was the velocity of the 1.0 kg block before the collision?

1. 3.5 m/s , in opposite direction of first ball
2. 2.5 m/s , in same direction of first ball
3. 2.5 m/s , in opposite dirction of first ball
4. 0 m/s, at rest

Q. A body of mass $m\text{kg}$ starts falling from a point $2R$ above the earth's surface. Its kinetic energy when it has fallen to a point $R$ above the earth's surface will be

1. $\frac{1}{2}\frac{GmM}{R}$
2. $\frac{1}{6}\frac{GmM}{R}$
3. $\frac{2}{3}\frac{GmM}{R}$
4. $\frac{1}{3}\frac{GmM}{R}$

Q.

The linear momentum of an object of mass $2\mathrm{kg}$ is $10\mathrm{kg}{\mathrm{ms}}^{-1}$. The velocity of the object is :

1. $2{\mathrm{ms}}^{-1}$

2. $20{\mathrm{ms}}^{-1}$

3. $5{\mathrm{ms}}^{-1}$

4. $10{\mathrm{ms}}^{-1}$

Q. A small ball falling vertically downward with constant velocity $4m/s$ strikes elastically a massive inclined cart moving with velocity $4m/s$ horizontally as shown. the velocity of the rebounded of the ball is

1. $4\sqrt{2}m/s$
2. $4\sqrt{3}m/s$
3. $4m/s$
4. $4\sqrt{5}m/s$

Q. A bomb of mass 20 kg is moving with a velocity of 10m/s on a straight path and suddenly explodes into two fragments. One moves in the same direction with a velocity of 40m/s and other in opposite direction with velocity 20m/s. Find the magnitude of masses .

Q. Two drivers spot in front of each other 80m apart they are travelling at 70 kmph and 60 kmph both apply brakes simultaneously which retard the cars at the rate of 5 metre per second square. which of the following statements is correct? (1)The collision will be averted(2)the collision will take place (3) they will cross Each Other (4)they will just collide

Q. A policeman moving on a highway with a speed of $30{\text{kmh}}^{-1}$ fires a bullet at a thief's car speeding away in the same direction with a speed of $192{\text{kmh}}^{-1}$. If the muzzle speed of the bullet is $150{\text{ms}}^{-1}$ with what speed does the bullet hit the thief's car?

1. $120\text{m/s}$
2. $90\text{m/s}$
3. $125\text{m/s}$
4. $105\text{m/s}$

Q. A mass $m$ moves with a velocity $v$ and collides inelastically with another identical mass. After collision, the 1st 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

1. $\frac{v}{\sqrt{3}}$
2. $\frac{2v}{\sqrt{3}}$
3. v$\sqrt{\frac{2}{3}}$
4. The situation of the problem is not possible without external impulse

Q.

Two small particles A & B of masses M and 2M respectively are joined rigidly to the ends of a light rod of length l as shown in the figure. The system translates on a smooth horizontal surface with a velocity u in a direction perpendicular to the rod. A particle P of mass M kept at rest on the surface sticks to the particle ‘A’ after collision with it. Then choose the correct option(s):

1. The speed of particle A just after collision is $\frac{u}{2}$ .

2. The speed of particle B just after collision is $\frac{u}{2}$ .

3. The velocity of centre of mass of system A + B + P is $\frac{3u}{4}$

4. The angular velocity of the system A + B + P after collision is $\frac{u}{2l}$

Q. A block of mass $m$ moving at a speed $v$ collides with another block of mass $2m$ at rest. The lighter block comes to rest after collision. What is the coefficient of restitution.

Q.

A particle of mass m is moving along the side of a square of side ‘a’, with a uniform speed v in the x-y plane as shown in the figure:

Which of the following statement is false for the angular momentum $\overrightarrow{L}$ about the origin?

1. when the particle is moving from C to D.

2. when the particle is moving from B to C.

3. when the particle is moving from D to A.

4. when the particle is moving from A to B.

Q. Two particles of masses $m_1,m_2$ movie with initial velocities $u_1\text{and}{u}_2$.On collision, one of the particles get excited to higher level, after absorbing energy If final velocities of particles be $v_1$ and $v_2$ then we must have :

1. $\frac{1}{2}{m}_1{u}_1^2+\frac{1}{2}{m}_2{u}_2^2=\frac{1}{2}{m}_1{v}_1^2+\frac{1}{2}{m}_2{v}_2^2-\epsilon$
2. $\frac{1}{2}{m}_1{u}_1^2+\frac{1}{2}{m}_2{u}_2^2+\epsilon =\frac{1}{2}{m}_1{v}_1^2+\frac{1}{2}{m}_2{v}_2^2$
3. $\frac{1}{2}{m}_1^2{u}_1^2+\frac{1}{2}{m}_2^2{u}_2^2-\epsilon =\frac{1}{2}{m}_1^2{v}_1^2+\frac{1}{2}{m}_2^2{v}_2^2$
4. $m_1^2{u}_1+m_2^2{u}_2-\epsilon =m_1^2{v}_1+m_2^2{v}_2$

Q. A heavy ball is thrown on a rough horizontal surface in such a way that it slides with a speed $V_0$ initially without rolling. It will roll without sliding when its speed fall to :

1. $\left(2/7\right)V_0$
2. $\left(3/7\right)V_0$
3. $\left(5/7\right)V_0$
4. $\left(7/5\right)V_0$

Q.

A boy of mass $60kg$ running at $3m/s$ jumps on a trolley of mass $140kg$ moving with a velocity of $1.5m/s$ in the same direction. What is their common velocity?

Q. Assertion :A particle strikes head-on with another stationary particle such that the first particle comes to rest after collision. The collision should necessarily be elastic. Reason: In elastic collision, there is a loss of momentum of the system of the particles.

1. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
2. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
3. Assertion is correct but Reason is incorrect
4. Both Assertion and Reason are incorrect

Q. A steel ball of mass 0.5 kg is dropped from a height of 4 m on to a horizontal heavy steel slap. the strile the slap and reounds to its original height.
(a) calculate the impulse delivered to the ball during impact.
(b) if the ball is in contact with the slab for 0.002 , find the average reaction force on the ball during impact.

Q. A particle of mass m moving towards the east with speed v collides with another particle of the same mass and same speed v moving towards the north. If the two particles stick to each other, the new particle of mass $2m$ will have a speed of?

1. $v$
2. $v\sqrt{2}$
3. $v/2$
4. $\frac{v}{\sqrt{2}}$

Q. A 2 kg mass moving on a smooth frictionless surface with a velocity of $10m{s}^{-1}$ hits another 2 kg mass kept at rest, in an inelastic collision. After collision, if they move together,

1. they travel with a velocity of $5m{s}^{-1}$ in the same direction
2. they travel with a velocity of $10m{s}^{-1}$ in the same direction
3. they travel with a velocity of $10m{s}^{-1}$ in the opposite direction
4. they travel with a velocity of $5m{s}^{-1}$ in the opposite direction

Q. three idntical spherical ball A, B, C are placed on a table as shown in the figure along a straight line . B and C are at rest initilly . the ball A hits B head -on with a speed of 10 ms ${}^{-1}$.then after all collision s( assumed to be elastic )A and B are brought to rest and C takes off with a velocity of

1. $5m{s}^{-1}$
2. $10m{s}^{-1}$
3. $2.5m{s}^{-1}$
4. $7.5m{s}^{-1}$

Q. A ball of mass $m$ moving at a speed $v$ makes a head on collision with an identical ball at rest. The kinetic energy of the balls after the collision is 3/4 of the original kinetic energy. Calculate the coefficient of restitution.

Q. Two particles of mass m, constrained to move along the circumference of a smooth circular hoop of equal mass m, are initially located at opposite ends of a diameter and given equal velocities $v_0$ shown in the figure. The entire arrangement is located in gravity free space. Their velocity just before collision is?

1. $\frac{1}{\sqrt{3}}{v}_0$
2. $\frac{\sqrt{3}}{2}{v}_0$
3. $\frac{2}{\sqrt{3}}{v}_0$
4. $\frac{\sqrt{7}}{3}{v}_0$