Collision Examples I

Q. If the Kinetic energy of a moving body becomes four times its initial Kinetic energy, then the percentage change in its momentum will be :

1. $100\text{\%}$
2. $200\text{\%}$
3. $300\text{\%}$
4. $400\text{\%}$

Q. A block of mass $1.9\text{kg}$ is at rest at the edge of a table, of height $1\text{m}$. A bullet of mass $0.1\text{kg}$ collides with the block and sticks to it. If the velocity of the bullet is $20{\text{ms}}^{-1}$ in the horizontal direction just before the collision then the kinetic energy, just before the combined system strikes the floor, is [Take $g=10{\text{ms}}^{-2}$]. Assume there is no rotational motion and losses of energy after the collision is negligible.

1. $20\text{J}$
2. $21\text{J}$
3. $19\text{J}$
4. $23\text{J}$

Q. A particle of mass $2m$ is projected at an angle of ${45}^{\circ }$ with horizontal with a velocity of $20\sqrt{2}{\text{ms}}^{-1}$. After $1\text{s}$ explosion takes place and the particle is broken into two equal pieces. As a result of the explosion, one part comes to rest. Find the maximum height $\left(\text{in metre}\right)$ from initial point of the particle, attained by the other part is
[Take $g=10{\text{ms}}^{-2}$]

Q.

As temperature increases, kinetic energy decreases.

1. True
2. False

Q. A metal ball of mass $2\text{kg}$ moving with speed of $36\text{kmph}$ is having a collision with a stationary ball of mass $2\text{kg}$. If after collision, both the balls move together, the loss in kinetic energy due to collision is:

1. $60\text{J}$
2. $160\text{J}$
3. $80\text{J}$
4. $40\text{J}$

Q. In an elastic collision

1. The kinetic energy first increases then decreases.
2. The initial kinetic energy is equal to the final kinetic energy
3. The final kinetic energy is less than the initial kinetic energy
4. The kinetic energy remains constant

Q. After a totally inelastic collision, two objects of the same masses and same initial speeds are found to move together at half of their initial speeds as shown in figure below. If $\alpha ={30}^{\circ }$, then the angle between the initial velocities of the objects is

1. ${90}^{\circ }$
2. ${60}^{\circ }$
3. ${150}^{\circ }$
4. ${45}^{\circ }$

Q.

A shell of mass $1\text{kg}$ is projected with velocity $20\text{m/s}$ at an angle ${60}^{\circ }$ with horizontal. It collides inelastically with a ball of mass $1\text{kg}$ which is suspended through a thread of length $1\text{m}$. The other end of the thread is attached to the ceiling of a trolley of mass $\frac{4}{3}\text{kg}$ as shown in figure. Initially the trolley is stationary and it is free to move along horizontal rails without any friction. What is the maximum deflection of the thread with vertical? String does not slack. Take $g=10{\text{m/s}}^2$.

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

Q. After perfectly inelastic collision between two identical particles, moving with the same initial speed in different directions, the speed of the composite particle becomes half the initial speed of an individual particle. Find the angle made by velocity of both the particles with $x-$axis before collision.

1. ${45}^{\circ }$
2. ${60}^{\circ }$
3. ${75}^{\circ }$
4. ${30}^{\circ }$

Q. A bullet hits a wooden block and loses half its velocity after penetrating 3cm. How much more will it penetrate before coming to rest?
Can we Solve this with work energy theorem?

Q.

A bomb of mass 10Kg explodes into two pieces of masses 4Kg and 6Kg . If kinetic energy of 4Kg piece is 200J. Find out kinetic energy of 6Kg piece

A.)400/3J B.)200/3J. C.)100/3J. D.)300/5J

Q. The kinetic energy of a projectile at its highest position is K. If the range of the projectile is 4 times the height of the projectile then find the initial kinetic energy of the projectile .

Q. Two particles, of masses $M$ and $2M$, moving, as shown, with speeds of $10\text{m/s}$ and $5\text{m/s}$, collide elastically at the origin. After the collision, they move along the indicated directions with speeds $v_1$ and $v_2$, respectively. The values of $v_1$ and $v_2$ are nearly

1. $3.2\text{m/s}$ and $12.6\text{m/s}$
2. $3.2\text{m/s}$ and $6.3\text{m/s}$
3. $6.5\text{m/s}$ and $6.3\text{m/s}$
4. $6.5\text{m/s}$ and $3.2\text{m/s}$

Q.

Two trucks of mass M each are moving in opposite direction on adjacent parallel tracks with same velocity u. One is carrying potatoes and other is carrying onions, bag of potatoes has a mass $m_1$ and bag of onions has a mass $m_2$ (included in the mass of truck M). When trucks get close to each other while passing, the drivers exchange a bag with the other one by throwing the other one. Find the final velocities of the trucks after exchange of the bags.

1. ,

2. ,

3. ,

4. ,

Q. The masses of Blocks $\text{A}$ , $\text{B}$ and $\text{C}$ are in the ratio $1:1:4$ . Block $\text{A}$ is given an initial velocity $v_0$ towards $\text{B}$ due to which it collides with $\text{B}$ perfectly inelastically. The combined mass collide with $\text{C}$ , also perfectly inelastically . If the loss in kinetic energy is $n$ times the initial kinetic energy , then the value of $n$ is

1. $\frac{3}{4}$
2. $\frac{4}{3}$
3. $\frac{5}{6}$
4. $\frac{6}{5}$

Q. A particle of mass $2\text{kg}$ moving in positive x-direction with speed $6\text{m/s}$ is hit by another particle of mass $4\text{kg}$ moving in the positive y-direction with speed $3\text{m/s}$. If the collision is perfectly inelastic, the percentage loss in energy during the collision is close to

1. 50%
2. 44%
3. 62%
4. 56%

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 $2.5\mathrm{m}{\mathrm{s}}^{-1}$ before the collision during which they stick together. What will be the velocity of the combined object after collision?

Q.

Two discs of moments of inertia I₁ and I₂ about their respective axes (normal to the disc and passing through the centre), and rotating with angular speeds ω₁ and ω₂ are brought into contact face to face with their axes of rotation coincident. (a) What is the angular speed of the two-disc system? (b) Show that the kinetic energy of the combined system is less than the sum of the initial kinetic energies of the two discs. How do you account for this loss in energy? Take ω₁ ≠ ω₂.

Q. Two particles of equal mass $m$, have respective initial velocities $u\hat{i}$ and $u\left(\frac{\hat{i}+\hat{j}}{2}\right).$ They collide completely inelastically. The energy lost in the process is:

1. $\frac{1}{3}m{u}^2$
2. $\frac{1}{8}m{u}^2$
3. $\frac{3}{4}m{u}^2$
4. $\sqrt{\frac{2}{3}}m{u}^2$

Q. A body of mass $2\text{kg}$ moving with a velocity $3\text{m/s}$ collides with a body of mass $1\text{kg}$ moving with a velocity of $4\text{m/s}$ in opposite direction. If the collision is head on and completely inelastic, then

1. Both particles move together with velocity $\left(\frac{2}{3}\right)\text{m/s}$
2. The momentum of system is $2\text{kg m/s}$ throughout
3. The momentum of system is $10\text{kg m/s}$
4. The loss of KE of system is $\left(\frac{49}{3}\right)J$

Q. A bullet in motion hits and gets embedded in a solid resting on a frictionless table. Which physical quantity is conserved?

1. Momentum and kinetic energy
2. Momentum alone
3. Kinetic energy alone
4. Neither momentum nor kinetic energy

Q. Three objects \(\text{A, B}\) and \(\text C\) are kept in a straight line on a frictionless horizontal surface. The masses of \(\text{A, B}\) and \(\text C\) are \(m, ~2~m\) and \(2~m\) respectively. \(\text A\) moves towards \(\text B\) with a speed of \(9~\text{m/s}\) and makes an elastic collision with it. Thereafter \(\text B\) makes a completely inelastic collision with \(\text C\). All motions occur along same straight line. The final speed of \(\text C\) is :

Q. A metal ball of mass 2 kg moving with speed of 36 km/hr is having a collision with a stationary ball of mass 3 kg. If after collision, both the balls move together, the loss in kinetic energy due to collision is :

1. $80J$
2. $60J$
3. $40J$
4. $160J$

Q. Two bodies of equal masses and speeds collide head-on elastically. Total momentum after collision is

1. non-zero
2. zero
3. can be zero or non-zero
4. insufficient data

Q.

(a) A child stands at the centre of a turntable with his two arms outstretched. The turntable is set rotating with an angular speed of 40 rev/min. How much is the angular speed of the child if he folds his hands back and thereby reduces his moment of inertia to 2/5 times the initial value? Assume that the turntable rotates without friction.

(b) Show that the child’s new kinetic energy of rotation is more than the initial kinetic energy of rotation. How do you account for this increase in kinetic energy?

Q. A small particle of mass $m=2\text{kg}$ moving with constant horizontal velocity $u=10{\text{ms}}^{-1}$ strikes a wedge shaped block of mass $M=4\text{kg}$ placed on the smooth surface as shown in figure. After collision, the particle starts moving up the inclined plane. Find the velocity of the wedge immediately after collision-

1. $1{\text{ms}}^{-1}$
2. $3{\text{ms}}^{-1}$
3. $2{\text{ms}}^{-1}$
4. $4{\text{ms}}^{-1}$

Q. A running man has half the kinetic energy of that of a boy of half of his mass. The man speeds up by $1m/s$, so that he has same kinetic energy as that of the boy. The original speed of the man is?

1. $(\sqrt{2}-1)m/s$
2. $\sqrt{2}m/s$
3. $\frac{1}{(\sqrt{2}-1)}m/s$
4. $\frac{1}{\sqrt{2}}m/s$

Q. In an inelastic collsion

1. The initial kinetic energy is equal to the final kinetic energy
2. The final kinetic energy is less than the initial kinetic energy
3. The kinetic energy remains the constant
4. The kinetic energy first increases then decreases.

Q. After a totally inelastic collision, two objects of the same masses and same initial speeds are found to move together at half of their initial speeds as shown in figure below. If $\alpha ={30}^{\circ }$, then the angle between the initial velocities of the objects is

1. ${90}^{\circ }$
2. ${60}^{\circ }$
3. ${150}^{\circ }$
4. ${45}^{\circ }$

Q. A ball of mass $m_1$ experiences a perfectly elastic collision with a stationary ball of mass $m_2$. What fraction of the K.E. does the striking ball lose, if the collision is head-on one.