(C) For a perfectly elastic collision in one dimension,the final velocity $v_2$ of the target mass $m_2$ (initially at rest) is given by the formula:$

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(C) For a perfectly elastic collision in one dimension,the final velocity $v_2$ of the target mass $m_2$ (initially at rest) is given by the formula:$v_2 = \left( \frac{2m_1}{m_1 + m_2} \right) u_1$Here,$m_1 = M$,$m_2 = m$,$u_1 = u$,and $u_2 = 0$.Substituting these values into the formula:$v = \left( \frac{2M}{M + m} \right) u$To match the given options,divide the numerator and denominator of the fraction by $M$:$v = \frac{2u}{\frac{M+m}{M}} = \frac{2u}{1 + \frac{m}{M}}$Thus,the correct option is $C$.

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

Difficult

$A$ sphere of mass $M$ moving with velocity $u$ undergoes a perfectly elastic collision with a stationary sphere of mass $m$. If their velocities after the collision are $V$ and $v$ respectively,what is the value of $v$?

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

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Work, Energy, Power and Collision

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Elastic Collision

$A$ body of mass $m$ moving with velocity $v$ makes a head-on collision with another body of mass $2m$ which is initially at rest. What is the ratio of the kinetic energy of the colliding body before and after the collision (in $: 1$)?

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$A$ billiard table has length and width as shown in the figure. $A$ ball is placed at point $A$. At what angle $\theta$ should the ball be projected so that after colliding with two walls,the ball will fall into the pocket $B$? Assume that all collisions are perfectly elastic and neglect friction.

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Five identical elastic balls are suspended in a row with strings of equal length such that the distance between the sides of the balls is very small. If the ball at the right end is released from one side,then:

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$A$ neutron moving with velocity $u$ collides elastically with a stationary atom of mass number $A$. If the collision is head-on and the initial kinetic energy of the neutron is $E$, then the final kinetic energy of the neutron after the collision is:

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$A$ sphere of mass $M$ moving with velocity $u$ undergoes a perfectly elastic collision with a stationary sphere of mass $m$. If their velocities after the collision are $V$ and $v$ respectively,what is the value of $v$?

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$A$ body of mass $m$ moving with velocity $v$ makes a head-on collision with another body of mass $2m$ which is initially at rest. What is the ratio of the kinetic energy of the colliding body before and after the collision (in $: 1$)?

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$A$ billiard table has length and width as shown in the figure. $A$ ball is placed at point $A$. At what angle $\theta$ should the ball be projected so that after colliding with two walls,the ball will fall into the pocket $B$? Assume that all collisions are perfectly elastic and neglect friction.

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