2D Collision Example

Q.

An object of mass $1\mathrm{kg}$ travelling in a straight line with a velocity of $10\mathrm{m}/\mathrm{s}$ collides with, and sticks to, a stationary wooden block of mass $5\mathrm{kg}$. Then they both move off together in the same straight line. Calculate the total momentum just before the impact and just after the impact. Also, calculate the velocity of the combined object.

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 ${90}^{\circ }$
2. More than ${90}^{\circ }$
3. Exactly ${90}^{\circ }$
4. Exactly ${180}^{\circ }$

Q. Which of the following quantities remains constant in a collision?

1. Kinetic energy
2. Momentum
3. Temperature
4. Both (a) and (b)

Q. In the figure shown below, two identical balls of mass $M$ and radius $R$ each, are placed in contact with each other on the frictionless horizontal surface. The third ball of mass $M$ and radius $R/2$, is coming down vertically and has a velocity $v_0$ when it hits the two balls symmetrically and itself comes to rest. Then, each of the two bigger balls will move after collision with a speed equal to

1. $\frac{4v_0}{\sqrt{3}}$
2. $\frac{2v_0}{\sqrt{3}}$
3. $\frac{v_0}{\sqrt{3}}$
4. $\sqrt{3}{v}_0$

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

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