COM in Oblique Collision

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. 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. 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.

Two putty balls of equal masses 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. $45\sqrt{2}m{s}^{-1}$

2. $45m{s}^{-1}$

3. $90m{s}^{-1}$

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

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. A ball of mass $m$ is suspended by a massless string of length $l=10\text{m}$ from a fixed point as shown in the figure below. A ball of mass $2m$ strikes at an angle $\theta ={45}^{\circ }$ from the horizontal and sticks to it. If the system deflects by angle $\varphi =\frac{\pi }{2}$, then the velocity of the system just after the collision and the velocity of $2m$ particle before collision are, respectively $\left(\text{in m/s}\right)$

1. $10\sqrt{2},30$
2. $10,30\sqrt{2}$
3. $10,30$
4. $10\sqrt{2},30\sqrt{2}$

Q.

Two putty balls of equal masses 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. $45\sqrt{2}m{s}^{-1}$

2. $45m{s}^{-1}$

3. $90m{s}^{-1}$

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