Bouncing Ball Example

Q. A ball is dropped from a height $h$ on to a floor. If in each collision its speed becomes $e$ times of its striking value, then total change in momentum of ball when it stops rebounding is (Here, $e$ is coefficient of restitution between the ball and the floor)

1. $m\sqrt{2gh}\left(\frac{e}{e(1+e)}\right)$
2. $\sqrt{2mgh}\left(\frac{e}{1-e}\right)$
3. $m\sqrt{2gh}\left(\frac{2e}{1+e}\right)$
4. $m\sqrt{2gh}\left(\frac{1+e}{1-e}\right)$

Q. A ball is dropped from a height $h$ on to a floor. If in each collision its speed becomes $e$ times of its striking value, then time taken by ball to stop rebounding is (Here, $e$ is coefficient of restitution between the ball and the floor)

1. $\sqrt{\frac{2h}{g}}\left(\frac{1+e}{1-e}\right)$
2. $\sqrt{\frac{h}{g}}\left(\frac{2-e}{2+e}\right)$
3. $\sqrt{2gh}\left(\frac{2-e}{2+e}\right)$
4. $\sqrt{\frac{h}{g}}\left(\frac{e}{1-e}\right)$

Q. A ball is dropped from a height $h$ on to a floor. If in each collision its speed becomes $e$ times of its striking value, then total change in momentum of ball when it stops rebounding is (Here, $e$ is coefficient of restitution between the ball and the floor)

1. $m\sqrt{2gh}\left(\frac{e}{e(1+e)}\right)$
2. $\sqrt{2mgh}\left(\frac{e}{1-e}\right)$
3. $m\sqrt{2gh}\left(\frac{2e}{1+e}\right)$
4. $m\sqrt{2gh}\left(\frac{1+e}{1-e}\right)$

Q. A ball initially at rest, is dropped from building of height $10\text{m}$ to ground as shown in the figure below. If the coefficient of restitution is $e=0.7$ and after collision, the ball rebounds back up to height $h$, find the value of $h$. (Take $g=9.8{\text{m/s}}^2)$

1. $10\text{m}$
2. $4.9\text{m}$
3. $9.8\text{m}$
4. $\text{None of these}$

Q.

A body falls from a height h on a horizontal surface and rebounds. Then it falls again and rebounds and so on. If the restitution coefficient is $\frac{1}{3}$, the total distance covered by the body before it comes to rest is

1. $\frac{h}{4}$

2. $\frac{5h}{4}$

3. $2h$

4. $3h$

Q. A ball is dropped from a height of $30\text{m}$ in downward direction on the stationary floor. If the value of coefficient of restitution is $0.6$ and ball rebounds back up to the height $\left(h^{\prime }\right)$, find the height $\left(h^{\prime }\right)$ after first collision.
(Take $g=10{\text{m/s}}^2$)

1. $21.6\text{m}$
2. $22.8\text{m}$
3. $10.8\text{m}$
4. $26.8\text{m}$

Q. A ball falling freely from a height of $4.9\text{m}$, hits a horizontal surface. If $e=\frac{3}{4}$, then the ball will hit the surface, second time after

1. $2.0\text{s}$
2. $1.0\text{s}$
3. $1.5\text{s}$
4. $3.0\text{s}$

Q. A ball falling freely from a height of $4.9\text{m}$, hits a horizontal surface. If $e=\frac{3}{4}$, then the ball will hit the surface, second time after

1. $1.0\text{s}$
2. $1.5\text{s}$
3. $2.0\text{s}$
4. $3.0\text{s}$

Q.

A ball is dropped from a height $h_0$ on a horizontal floor and keeps rebounding after hitting the floor. Find: (i) speed after $n$ rebounds

(ii) Total distance travelled by the ball before stopping

(iii) Height it rises after nth rebound

(iv) Total time before stopping

(coefficient of restitution is $e$)

1. (i) $e^n\sqrt{2g{h}_0}$, (ii)$e^{2n}{h}_0$, (iii) $h_0\left[\frac{1+e^2}{1-e^2}\right]$, (iv) $\left(\frac{1+e}{1-e}\right)\sqrt{\frac{2h_0}{g}}$

2. (i) $e^{2n}\sqrt{2g{h}_0}$, (ii)$e^{4n}{h}_0$, (iii) $h_0\left[\frac{1-e^2}{1+e^2}\right]$, (iv) $\left(\frac{1+e}{1-e}\right)\sqrt{\frac{2h_0}{g}}$

3. (i)$e^n\sqrt{2g{h}_0}$, (ii)$e^{-4n}{h}_0$, (iii)infinite (iv) infinite

4. None of these

Q.

A body falls from a height h on a horizontal surface and rebounds. Then it falls again and rebounds and so on. If the restitution coefficient is $\frac{1}{3}$, the total distance covered by the body before it comes to rest is

1. $\frac{h}{4}$

2. $\frac{5h}{4}$

3. $2h$

4. $3h$

Q.

A ball is dropped from a height $h_0$ on a horizontal floor and keeps rebounding after hitting the floor. Find: (i) speed after $n$ rebounds

(ii) Total distance travelled by the ball before stopping

(iii) Height it rises after nth rebound

(iv) Total time before stopping

(coefficient of restitution is $e$)

1. (i) $e^n\sqrt{2g{h}_0}$, (ii)$e^{2n}{h}_0$, (iii) $h_0\left[\frac{1+e^2}{1-e^2}\right]$, (iv) $\left(\frac{1+e}{1-e}\right)\sqrt{\frac{2h_0}{g}}$

2. (i) $e^{2n}\sqrt{2g{h}_0}$, (ii)$e^{4n}{h}_0$, (iii) $h_0\left[\frac{1-e^2}{1+e^2}\right]$, (iv) $\left(\frac{1+e}{1-e}\right)\sqrt{\frac{2h_0}{g}}$

3. (i)$e^n\sqrt{2g{h}_0}$, (ii)$e^{-4n}{h}_0$, (iii)infinite (iv) infinite

4. None of these

Q. A ball falls on the ground from a height of $2.0\text{m}$ and rebounds up to a height of $1.5\text{m}$. Find the coefficient of restitution for the collision of the ball with the ground. Take $g=10{\text{m/s}}^2$.

1. $\frac{1}{2}$
2. $\frac{\sqrt{3}}{2}$
3. $1$
4. $0$

Q. A ball initially at rest, is dropped from building of height $10\text{m}$ to ground as shown in the figure below. If the coefficient of restitution is $e=0.7$ and after collision, the ball rebounds back up to height $h$, find the value of $h$. (Take $g=9.8{\text{m/s}}^2)$

1. $10\text{m}$
2. $4.9\text{m}$
3. $9.8\text{m}$
4. $\text{None of these}$

Q. A ball initially at rest falls from a height $h=2.5\text{m}$. After collision with surface having value of coefficient of restitution $e=0.6$, it rebounds back. Find the rebound velocity of ball.

1. $2\text{m/s}$
2. $4.2\text{m/s}$
3. $6\text{m/s}$
4. $11.66\text{m/s}$

Q. A ball is projected from a point in one of the two smooth parallel vertical walls against the other in a plane perpendicular to both. After being reflected at each wall impinge again on the second at a point in the same plane as it started. The distance between two walls is $a.b$ is the free range and $e$ be the coefficient of restitution:

1. The total time taken in moving from $O$ to $C$ is $\frac{a}{e^{2}u}(e^2+e+1)$
2. The free range on the horizontal plane $b=\frac{2uv}{g}$
3. $b{e}^2=a(e^2+e+1)$
4. All of these

Q. A ball is dropped from a height of $45\text{m}$ from the ground. The coefficient of restitution beween the ball and the ground is $\frac{2}{3}$. What is the distance in m travelled by the ball in 4th second of its motion? Assume negligible time is spent in rebounding. Let $g=10m/s^2.$

Q. A body falls from a height 'h' on a horizontal surface and rebounds. Then it falls again and again rebounds and so on. If the restitution coefficient is $\frac{1}{3}$, the total time taken by the body to come to rest is

1. $\sqrt{\frac{2h}{g}}$
2. $2\sqrt{\frac{2h}{g}}$
3. $3\sqrt{\frac{2h}{g}}$
4. $4\sqrt{\frac{2h}{g}}$

Q. A body falls from a height 'h' on a horizontal surface and rebounds. Then it falls again and again rebounds and so on. If the restitution coefficient is $\frac{1}{3}$, the total distance covered by the body before it comes to rest is

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