(D) For an elastic collision,the coefficient of restitution $e = 1$.The velocity of approach is $u_{rel} = v_1 - v_2$.Since the block is very heavy,it

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$2v_2 - v_1$ in the original direction

(D) For an elastic collision,the coefficient of restitution $e = 1$.The velocity of approach is $u_{rel} = v_1 - v_2$.Since the block is very heavy,its velocity remains effectively unchanged after the collision,i.e.,$V_{block} \approx v_2$.Let the final velocity of the particle be $v'$.The velocity of separation is $v_{rel} = V_{block} - v' = v_2 - v'$.Since $e = \frac{v_{rel}}{u_{rel}}$,we have $1 = \frac{v_2 - v'}{v_1 - v_2}$.Therefore,$v_1 - v_2 = v_2 - v'$.Solving for $v'$,we get $v' = 2v_2 - v_1$.

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

Medium

$A$ 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:

A
$2v_1 - v_2$ in the original direction
B
$v_1 - v_2$ in the original direction
C
$v_2 - 2v_1$ in the original direction
D
$2v_2 - v_1$ in the original direction

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Elastic Collision

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$A$ sphere $P$ of mass $m$ moving with velocity $v$ undergoes an oblique and perfectly elastic collision with an identical sphere $Q$ initially at rest. The angle $\theta$ between the velocities of the spheres after the collision shall be .............. $^o$.

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The bob $A$ of a simple pendulum is released when the string makes an angle of $45^o$ with the vertical. It hits another bob $B$ of the same material and same mass kept at rest on the table. If the collision is elastic,then

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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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$A$ 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 $: 1$)?

$A$ particle of mass $m$ moving with velocity $\vec{v_1}$ undergoes a two-dimensional elastic collision with another particle of mass $m$ at rest. If the particles move with velocities $\vec{v_1}'$ and $\vec{v_2}'$ after the collision,what is the angle between them in degrees?

$A$ sphere $P$ of mass $m$ moving with velocity $v$ undergoes an oblique and perfectly elastic collision with an identical sphere $Q$ initially at rest. The angle $\theta$ between the velocities of the spheres after the collision shall be .............. $^o$.

$A$ simple pendulum,made of a string of length $l$ and a bob of mass $m$,is released from a small angle $\theta_0$. It strikes a block of mass $M$,kept on a horizontal surface at its lowest point of oscillations,elastically. It bounces back and goes up to an angle $\theta_1$. Then $M$ is given by

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