2D Collision Example

Q.

A ball collides elastically with another ball of the same mass. The collision is oblique and initially second ball was at rest. After the collision, the two balls move with same speeds. What will be the angle between the velocities of the balls after the collision?

1. 

2. 

3. 

4. 

Q. A ball of mass 'm' moving with a velocity 'v' undergoes an oblique elastic collision with another ball of the same mass 'm' but at rest. After the collision, if the two balls move with different speeds after the collision, the angle between their directions of motion will be

1. Less than
2. More than
3. Exactly
4. Exactly

Q. A body of mass 'm' moving with a velocity 'v' in the x-direction collides with a body of mass 'M' moving with a velocity 'V' in the y-direction. They stick together during a collision. Then

1. All the above choices are correct.
2. The magnitude of the momentum of the composite body is
3. The composite body moves in a direction making a angle with the x-axis.
4. The loss of kinetic energy as a result of collision is

Q. A ball of mass 20 kg moving at 2 m/s horizontally strikes another ball of mass 12 kg at rest. If after the collision, the 20 kg ball is now moving with a velocity of 1 m/s at an angle of 30° with the horizontal. Find the final velocity of the 12 kg ball.

1. 2.54 i + 1.62 j
2. 2.54 i - 1.62 j
3. 1.89 i + 0.83 j
4. 1.89 i - 0.83 j

Q.

Two equal spheres of mass $m$ are in contact on a smooth horizontal table. A third identical sphere impinges symmetrically on them and is reduced to rest. Find the loss of K.E

1. 

2. 

3. 

4. 

Q.

A disc of mass $m$ is moving with constant speed $v_0$ on a smooth horizontal table. Another disc of same mass is placed on the table at rest as show in the figure. If collision is elastic then find the velocity of the discs after collision.

[Consider $r<<R$]$(\theta =ta{n}^{-1}\frac{h}{\sqrt{R^2-h^2}})$.

1. 0, v₀ sin θ

2. 0, v₀cosθ

3. v₀ sin θ, v₀cosθ

4. v₀, 0

Q. Two putty balls of equal masses moving with equal speeds in mutually perpendicular direction, stick together after collision. If the balls were initially moving with a speed of $45\sqrt{2}m{s}^{-1}$ each, the speed of their combined mass after collision is.

1. $45\sqrt{2}m{s}^{-1}$
2. $45m{s}^{-1}$
3. $90m{s}^{-1}$
4. $22.5\sqrt{2}m{s}^{-1}$

Q. Two balls are colliding obliquely. Assume that the balls are smooth and all other external forces are absent then,

1. The component of the momentum of system perpendicular to the line of impact is conserved.
2. The component of the momentum of each ball separately perpendicular to the line of impact is conserved.
3. Both (a) and (b) are correct.
4. Both (a) and (b) are incorrect.

Q. A sphere of mass $M=2\text{kg}$ moving with a velocity of $2\sqrt{2}\text{m/s}$ collides with another sphere of mass $m=1\text{kg}$ initially at rest at an angle of ${45}^{\circ }$ with the horizontal. If the coefficient of restitution of the collision is 0.5, what will be the final velocity(in $\text{m/s}$) of the sphere having mass $m$ ?

1. $-\sqrt{2}\hat{i}+\sqrt{2}\hat{j}$
2. $\sqrt{2}\hat{i}-\sqrt{2}\hat{j}$
3. $\sqrt{2}\hat{i}+\sqrt{2}\hat{j}$
4. $-\sqrt{2}\hat{i}-\sqrt{2}\hat{j}$

Q. A ball is thrown at a triangular wedge with an angle of inclination ${60}^o$ parallel to the ground as shown in the figure. After bouncing against the wedge, the velocity of the ball is perpendicular to the ground. What is the coefficient of restitution?

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