Bouncing Ball Example

Q. From a point on the ground, a ball is projected to hit smooth vertical wall. After collision, the ball returns to the point of projection. If total time of flight of ball is four times the time taken by the ball to reach the wall from point of projection, then the coefficient of restitution is $x$. Find the value of $\frac{1}{x}$.

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. 
2. 
3. 
4. 

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. 
2. 
3. 
4. 

Q.

A steel ball falls from a height ‘h’ on a floor for which the coefficient of restitution is e. The height attained by the ball after the first rebounds is

1. $h{e}^2$
2. $h/e$
3. $h/e^2$
4. $he$

Q.

A ball is dropped from a height of 1 m. If the coefficient of restitution of collision between the ball and the floor is 0.5. What is the total distance travelled by the ball before it comes to rest.

1. 5/3 m
2. 2/3 m
3. 7/3 m
4. 8/3 m

Q.

A ball drops from the ceiling of the room, and after rebounding twice from the floor, reaches a height equal to half that of ceiling. Find the coefficient of restitution?

1. 

2. 

3. 

4. 

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. None of these

2. (i) , (ii), (iii) , (iv)

3. (i) , (ii), (iii) , (iv)

4. (i), (ii), (iii)infinite (iv) infinite

Q. A steel ball falls from a height h on a floor for which the coefficient of restitution is e. The height attained by the ball after two rebounds is

1. 
2. 
3. 
4. 

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

2. $3h$

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

4. $2h$

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. $26.8\text{m}$
4. $10.8\text{m}$