(B) Let the mass of ball $2$ be $m$. Then the mass of ball $1$ is $2m$.Initial momentum $P_i = (2m)(v) + (m)(0) = 2mv$.Let the final velocity of ball

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(B) Let the mass of ball $2$ be $m$. Then the mass of ball $1$ is $2m$.Initial momentum $P_i = (2m)(v) + (m)(0) = 2mv$.Let the final velocity of ball $2$ be $v_2$. According to the law of conservation of momentum:$2mv = (2m)(v/3) + m(v_2)$$2v = 2v/3 + v_2$$v_2 = 2v - 2v/3 = 4v/3$.The coefficient of restitution $e$ is defined as the ratio of the relative velocity of separation to the relative velocity of approach:$e = (v_2 - v_1) / (u_1 - u_2)$$e = (4v/3 - v/3) / (v - 0) = (3v/3) / v = v / v = 1$.Since the coefficient of restitution $e = 1$,the collision is elastic.

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

Medium

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?

A
Inelastic
B
Elastic
C
Completely inelastic
D
Cannot be determined from the information given

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Work, Energy, Power and Collision

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Elastic Collision

An alpha-particle of mass $m$ undergoes a $1$-dimensional elastic collision with a nucleus of unknown mass $M$ at rest. It is scattered directly backwards,losing $64\%$ of its initial kinetic energy. The mass of the nucleus is .......... $m$.

DifficultJEE MAIN 2019

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Assertion $(A)$: In an elastic collision of two billiard balls,both kinetic energy and linear momentum remain conserved.
Reason $(R)$: During the collision of the balls,as the collision is elastic,there is no exchange of energy. Therefore,both energy and momentum are conserved.

EasyTS EAMCET 2022

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$A$ car of mass $400 \ kg$ is moving with a speed of $72 \ km/h$. It collides with a truck of mass $4000 \ kg$ moving in the same direction with a speed of $9 \ km/h$. After the collision,the car rebounds with a speed of $18 \ km/h$. Find the speed of the truck after the collision in $km/h$.

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An object $A$ of mass $20 \ kg$ and travelling at $20 \ m \ s^{-1}$ crashes into another object $B$ of mass $200 \ kg$ and travelling at $10 \ m \ s^{-1}$, in the same direction. After the collision, object $A$ bounces back in the opposite direction at a speed of $10 \ m \ s^{-1}$. The speed of the object $B$ after the collision is: (in $m \ s^{-1}$)

MediumTS EAMCET 2021

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$A$ body of mass $8 \ kg$ undergoes an elastic collision with a stationary body of mass $2 \ kg$. If the initial kinetic energy is $E$,then the kinetic energy remaining with the $8 \ kg$ body after the collision is ............ $E$.

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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?

Similar Questions

An alpha-particle of mass $m$ undergoes a $1$-dimensional elastic collision with a nucleus of unknown mass $M$ at rest. It is scattered directly backwards,losing $64\%$ of its initial kinetic energy. The mass of the nucleus is .......... $m$.

Assertion $(A)$: In an elastic collision of two billiard balls,both kinetic energy and linear momentum remain conserved.Reason $(R)$: During the collision of the balls,as the collision is elastic,there is no exchange of energy. Therefore,both energy and momentum are conserved.

$A$ car of mass $400 \ kg$ is moving with a speed of $72 \ km/h$. It collides with a truck of mass $4000 \ kg$ moving in the same direction with a speed of $9 \ km/h$. After the collision,the car rebounds with a speed of $18 \ km/h$. Find the speed of the truck after the collision in $km/h$.

$A$ body of mass $8 \ kg$ undergoes an elastic collision with a stationary body of mass $2 \ kg$. If the initial kinetic energy is $E$,then the kinetic energy remaining with the $8 \ kg$ body after the collision is ............ $E$.

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Assertion $(A)$: In an elastic collision of two billiard balls,both kinetic energy and linear momentum remain conserved.
Reason $(R)$: During the collision of the balls,as the collision is elastic,there is no exchange of energy. Therefore,both energy and momentum are conserved.