A sphere of mass m moving with velocity v col | vedclass

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

Question

(C) Let the mass of both spheres be $m$. The initial velocity of the first sphere is $v$ and the second sphere is $0$. Let their final velocities be $

Vedclass · Accepted Answer

$\frac{e+1}{2}$

Vedclass · Answer

(C) Let the mass of both spheres be $m$. The initial velocity of the first sphere is $v$ and the second sphere is $0$. Let their final velocities be $V_1$ and $V_2$ respectively.By the law of conservation of linear momentum:$m v + m(0) = m V_1 + m V_2$$v = V_1 + V_2$  --- $(1)$By the definition of the coefficient of restitution $e$:$e = \frac{V_2 - V_1}{u_1 - u_2}$$e = \frac{V_2 - V_1}{v - 0}$$e v = V_2 - V_1$ --- $(2)$Adding equations $(1)$ and $(2)$:$v + e v = (V_1 + V_2) + (V_2 - V_1)$$v(1 + e) = 2 V_2$$V_2 = \frac{v(e + 1)}{2}$The ratio of the final velocity of the second sphere $(V_2)$ to the initial velocity of the first sphere $(v)$ is:$\frac{V_2}{v} = \frac{e + 1}{2}$

$A$ sphere of mass $m$ moving with velocity $v$ collides head-on with another sphere of the same mass which is at rest. The ratio of the final velocity of the second sphere to the initial velocity of the first sphere is (where $e$ is the coefficient of restitution and the collision is inelastic).

Similar Questions

During an inelastic collision between two objects,which of the following quantities always remains conserved?

$A$ ball $P$ of mass $0.5 \ kg$ moving with a velocity of $10 \ ms^{-1}$ collides with another ball $Q$ of mass $1 \ kg$ at rest. If the coefficient of restitution is $0.4$,the ratio of the velocities of the balls $P$ and $Q$ after the collision is

An object is dropped from a height $h$ from the ground. Every time it hits the ground,it loses $50\%$ of its kinetic energy. The total distance covered as $t \to \infty$ is

$A$ ball of mass $m$ moving with velocity $v$ collides head-on with a second ball of mass $m$ at rest. If the coefficient of restitution is $e$,the velocity of the first ball after collision is $v_1$,and the velocity of the second ball after collision is $v_2$,then:

$A$ ball strikes a smooth horizontal ground at an angle of $45^o$ with the vertical. What cannot be the possible angle of its velocity with the vertical after the collision? (Assume $e \leq 1$ ).

Vedclass Test Series

Exam Paper Generator

Online Exam Module