A ball of mass m is moving with a speed V as | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(D) The collision occurs along the line joining the centers of the two balls. The angle between the velocity vector $V$ and the line of impact is $30^

Vedclass · Accepted Answer

$\frac{\sqrt{3}V}{4}$

Vedclass · Answer

(D) The collision occurs along the line joining the centers of the two balls. The angle between the velocity vector $V$ and the line of impact is $30^{\circ}$.The component of velocity along the line of impact is $u = V \cos 30^{\circ} = \frac{\sqrt{3}V}{2}$.Let $v_1$ be the velocity of the ball of mass $2m$ and $v_2$ be the velocity of the ball of mass $m$ along the line of impact after the collision.Applying the law of conservation of linear momentum along the line of impact:$m u = m v_2 + (2m) v_1$$u = v_2 + 2v_1$  --- $(1)$Applying the coefficient of restitution formula $(e = 1/2)$:$e = \frac{v_1 - v_2}{u}$$\frac{1}{2} = \frac{v_1 - v_2}{u}$$u = 2v_1 - 2v_2$ --- $(2)$Adding equations $(1)$ and $(2)$:$2u = 4v_1 - v_2 + v_2 = 4v_1$$v_1 = \frac{u}{2} = \frac{\sqrt{3}V}{2 	imes 2} = \frac{\sqrt{3}V}{4}$.

$A$ ball of mass $m$ is moving with a speed $V$ as shown in the figure. It undergoes an inelastic collision with a ball of mass $2m$ which was initially at rest. The velocity of the ball of mass $2m$ after the collision is given by

Similar Questions

$A$ ball is dropped from a height $h$ on a floor of coefficient of restitution $e$. The total distance covered by the ball just before the second hit is

$A$ moving ball collides head-on with a similar ball at rest. If $\frac{1}{4}$ of the kinetic energy is lost during the impact,the value of the coefficient of restitution is:

$A$ ball of mass $2 \ g$ moving with a velocity of $2 \ ms^{-1}$ collides with another ball of mass $8 \ g$ which is at rest and comes to rest after collision. Then the coefficient of restitution is

$A$ ball kept at $20 \,m$ height falls freely in a downward direction vertically and hits the ground. The coefficient of restitution is $0.4$. After the first rebound, the upward velocity is $[g = 10 \,m/s^2]$. (in $\,m/s$)

$A$ body falling from a height of $10\,m$ rebounds from a hard floor. If it loses $20\%$ of its energy in the impact,then the coefficient of restitution is:

Vedclass Test Series

Exam Paper Generator

Online Exam Module