(C) For a perfectly elastic head-on collision,the final velocity $v_2$ of the second body (mass $m_2$) is given by the formula:$v_2 = \left( \frac{2m_

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(C) For a perfectly elastic head-on collision,the final velocity $v_2$ of the second body (mass $m_2$) is given by the formula:$v_2 = \left( \frac{2m_1}{m_1 + m_2} \right) u_1 + \left( \frac{m_2 - m_1}{m_1 + m_2} \right) u_2$Here,$m_1 = M$,$m_2 = m$,$u_1 = u$,and $u_2 = 0$ (since the second sphere is at rest).Substituting these values into the formula:$v = \left( \frac{2M}{M + m} \right) u + \left( \frac{m - M}{M + m} \right) (0)$$v = \frac{2Mu}{M + m}$To match the given options,divide the numerator and denominator by $M$:$v = \frac{2u}{(M + m)/M} = \frac{2u}{1 + m/M}$

Class 11 Physics Work, Energy, Power and Collision Elastic Collision

Difficult

$A$ sphere of mass $M$ moving with velocity $u$ undergoes a perfectly elastic head-on collision with another sphere of mass $m$ at rest. After the collision,their velocities are $V$ and $v$ respectively. Find the value of $v$.

A
$2u \frac{M}{m}$
B
$2u \frac{m}{M}$
C
$\frac{2u}{1 + m/M}$
D
$\frac{2u}{1 + M/m}$

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Work, Energy, Power and Collision

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Elastic Collision

After a head-on elastic collision between two balls of equal masses,one is observed to have a speed of $3\,m/s$ along the positive $x$-axis and the other has a speed of $2\,m/s$ along the negative $x$-axis. What were the original velocities of the balls?

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$A$ uniform rod of mass $M$ and length $L$ is placed on a smooth horizontal surface. $A$ particle of mass $m$ moving with velocity $v$ strikes the rod at one end perpendicularly and comes to rest. The velocity of the centre of mass of the rod after the collision is:

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$A$ sphere of mass $m$,moving with velocity $3u$,collides head-on with another identical sphere at rest. If $e$ is the coefficient of restitution,what will be the ratio of the velocity of the second sphere to that of the first sphere after the collision?

MediumMHT CET 2025

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$A$ light particle moving horizontally with a speed $v_1$ strikes a very heavy block moving in the same direction with a speed $v_2$. The collision is elastic. After the collision,the velocity of the particle is:

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$A$ sphere of mass $M$ moving with velocity $u$ undergoes a perfectly elastic head-on collision with another sphere of mass $m$ at rest. After the collision,their velocities are $V$ and $v$ respectively. Find the value of $v$.

Similar Questions

After a head-on elastic collision between two balls of equal masses,one is observed to have a speed of $3\,m/s$ along the positive $x$-axis and the other has a speed of $2\,m/s$ along the negative $x$-axis. What were the original velocities of the balls?

$A$ ball of mass $2 \,kg$ collides with another ball of mass $M$ at rest. If the collision is elastic and after the collision, the first ball moves with $\frac{1}{3}$ of its initial velocity in the same direction, then the mass of the second ball is: (in $\,kg$)

$A$ uniform rod of mass $M$ and length $L$ is placed on a smooth horizontal surface. $A$ particle of mass $m$ moving with velocity $v$ strikes the rod at one end perpendicularly and comes to rest. The velocity of the centre of mass of the rod after the collision is:

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