The 'e' Equation

Q. Two identical balls $A$ and $B$ of equal masses are lying on a smooth horizontal surface as shown in the fig. Ball $A$ hits ball $B$ with a velocity $16{\text{ms}}^{-1}$. What should be the minimum value of coefficient of restitution ${}^{\prime }{e}^{\prime }$ between $A$ and $B$ so that $B$ just reaches the highest point of the inclined plane? Take $g=10{\text{ms}}^{-2}$.

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

Q.

A ball collides directly with another ball at rest and is itself brought to rest by the impact. If one fourth of initial kinetic energy is destroyed in the collision, the coefficient of restitution of the collision is

1. 

2. 

3. 

4. 

Q.

A metal ball falls from a height of 32 m on a steel plate. If the coefficient of restitution is 0.5, to what height will the ball rise after the second bounce

1. 2 m

2. 4 m

3. 8 m

4. 16 m

Q.

A ball strikes a wall with a velocity $\overrightarrow{u}$ at an angle $\theta$ with the normal to the wall surface and rebounds from it at an angle $\beta$ with the surface. Then:

1. > , if wall is smooth

2. If the wall is smooth, coefficient of restitution

3. If wall is smooth, coefficient of restitution <

4. none of these

Q.

The coefficient of restitution e for a perfectly elastic collision is

1. 1

2. 0

3. 

4. - 1

Q.

A block of mass $m$ moving at a velocity $v$ collides head on with another block of mass $2m$ at rest. If the coefficient of restitution is $\frac{1}{2}$, find the velocities of the blocks after the collision.

1. 

2. 

3. 

4. 

Q. A block of mass $m$ moving at a velocity $v$ collides head on with another block of mass $2m$ at rest. If the coefficient of restitution is $\frac{1}{2}$, the velocities of the blocks after the collision respectively are and .

1. \N
2. v/2
3. -v/2
4. v

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. The total distance travelled by the ball before it comes to rest is.

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

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 rebound is .

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

Q. Two equal spheres $A$ and $B$ lie on a smooth horizontal circular groove at opposite ends of a diameter. At time $t=0$, $B$ is projected along the groove and it first impinges on $A$ at time $t=T_1$ and again at time $t=T_2$. If $e$ is the coefficient of restitution, the ratio $\frac{T_2}{T_1}$ is

1. $\frac{2}{e}$
2. $\frac{(2+e)}{e}$
3. $\frac{2(e+1)}{e}$
4. $\frac{(2+e)}{2}$