A body of mass m moving with a velocity v col | vedclass

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

Question

(D) Let $v_1$ and $v_2$ be the velocities of the bodies of mass $m$ and $2m$ respectively after the collision.By the law of conservation of linear mom

Vedclass · Accepted Answer

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

Vedclass · Answer

(D) Let $v_1$ and $v_2$ be the velocities of the bodies of mass $m$ and $2m$ respectively after the collision.By the law of conservation of linear momentum: $mv + (2m)(0) = mv_1 + 2mv_2$,which simplifies to $v = v_1 + 2v_2$ (Equation $1$).The coefficient of restitution $e$ is defined as $e = \frac{v_2 - v_1}{u_1 - u_2}$.Given $u_1 = v$ and $u_2 = 0$,we have $e = \frac{v_2 - v_1}{v}$,which implies $v_1 = v_2 - ev$ (Equation $2$).Substitute Equation $2$ into Equation $1$: $v = (v_2 - ev) + 2v_2$.$v(1+e) = 3v_2$,so $v_2 = \frac{v(1+e)}{3}$.Now,substitute $v_2$ back into Equation $2$: $v_1 = \frac{v(1+e)}{3} - ev = \frac{v + ev - 3ev}{3} = \frac{v(1-2e)}{3}$.The ratio of the velocities $v_1/v_2$ is $\frac{v(1-2e)/3}{v(1+e)/3} = \frac{1-2e}{1+e}$.

$A$ body of mass $m$ moving with a velocity $v$ collides head-on with another body of mass $2m$ at rest. If the coefficient of restitution between the two bodies is $e$,then the ratio of the velocities of the two bodies after collision is:

Similar Questions

Particle $A$ makes a perfectly elastic collision with another particle $B$ at rest. They fly apart in opposite directions with equal speeds. If their masses are $m_A$ and $m_B$ respectively,then:

Two billiard balls undergo a head-on collision. Ball $1$ is twice as heavy as ball $2$. Initially,ball $1$ moves with a speed $v$ towards ball $2$ which is at rest. Immediately after the collision,ball $1$ travels at a speed of $v/3$ in the same direction. What type of collision has occurred?

In an elastic collision of two billiard balls,which of the following quantities is not conserved during the short time of collision?

During an elastic collision between two bodies,which of the following statements are correct?
$I$. The initial kinetic energy is equal to the final kinetic energy of the system.
$II$. The linear momentum is conserved.
$III$. The kinetic energy during $\Delta t$ (the collision time) is not conserved.

Vedclass Test Series

Exam Paper Generator

Online Exam Module