COM in Oblique Collision

Q.

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

1. 

2. 

3. 

4. 

Q. Two smooth spheres made of identical material having masses $m$ and $2m$ undergo an oblique impact as shown in figure. The initial velocities of the masses are also shown. The impact force is along the line joining their centres. The coefficient of restitution is 5/9. The velocities of the masses after the impact are:

1. $\frac{10}{3}\hat{i}+8j,\frac{5}{3}\hat{i}+\frac{4}{3}j,$
2. $\frac{5}{3}\hat{i}-8j,\frac{-5}{3}\hat{i}+4j,$
3. $\frac{10}{3}\hat{i}-8\hat{j},\frac{-5}{3}\hat{i}+4\hat{j},$
4. None of these

Q. The point B lies on a smooth plane inclined at ${30}^{\circ }$ to the horizontal. A particle of mass $\frac{1}{7}\text{kg}$ is dropped from a point A which lies $10\text{m}$ vertically above B. The particle rebounds from the plane in the direction BC with speed $v\text{m/s}$ at an angle of ${45}^{\circ }$ to the plane. Find the impulse exerted by the plane on the particle (in $\text{Ns}$)

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

Q. A ball $A$ collides elastically with another identical ball $B$ which is at rest initially with velocity $10\text{m/s}$ at an angle of ${30}^{\circ }$ with the line joining their centres $C_1$ and $C_2$. Select the correct alternative(s).

1. velocity of ball $A$ after collision is $5\text{m/s}$
2. velocity of ball $B$ after collision is $5\sqrt{3}\text{m/s}$
3. both the balls move at right angles after collision
4. kinetic energy will not be conserved here, because collision is not head on