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Two smooth balls A and B, each of mass m...

Two smooth balls A and B, each of mass m and radius R, have their centre at (0,0,R) and (5R,-R,R) respectively, in a coordinate system as shown. Ball A, moving along positive x-axis, collides with ball B. Just before the collision, speed of ball A is 4m/s and ball B is stationary. The collision between the balls is elastic. Velocity of the ball A just after the collsion is

A

`(i+sqrt(3)j)m//s`

B

`(i-sqrt(3)j)m//s`

C

`(2i+sqrt(3)j)m//s`

D

`(2i+2j)m//s`

Text Solution

Verified by Experts

The correct Answer is:
A
`v_(A)=4 sin 30^(@)[cos 60hat(i)+sin 60 hat(j)]`
`v_(A)=hat(i)+sqrt(3)hat(j)`

`therefore` (A)
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Knowledge Check

  • Two smooth balls A and B, each of mass m and radius R, have their centers at (0, 0, R) and at (5R, -R, R) respectively, in a coordinate system as shown. Ball A, moving along positive x axis, collides with ball B. Just before the collision, speed of ball A is 4m/s and ball B is stationary. The collision between the ball is elastic. Impulse of the force exerted by A and B during the collision, is equal to

    A
    `(sqrt(3)mi+3mj)kg-m//s`
    B
    `((sqrt(3))/(2)mi-sqrt(3)mj)kg-m//s`
    C
    `(3mi-sqrt(3)mj)kg-m//s`
    D
    `(2sqrt(3)mi+3mj)kg-m//s`

  • Two smooth balls A and B , each of mass m and radius R , have their centres as shown in fig. Ball A , moving along positive x-axis, collides with ball B . Just before the collision, speed of ball 'A' is 4m//s and ball 'B' is stantionary. The collision Velocity of the ball 'A' just after the collision is

    A
    `(i + sqrt(3)hat(j))m//s`
    B
    `(i - sqrt(3)hat(j))m//s`
    C
    `(2i + sqrt(3)hat(j))m//s`
    D
    `(2i + 2 hat(j))m//s`

  • Two smooth balls A and B , each of mass m and radius R , have their centres as shown in fig. Ball A , moving along positive x-axis, collides with ball B . Just before the collision, speed of ball 'A' is 4m//s and ball 'B' is stantionary. The collision What is velocity of ball 'B' after collision is

    A
    `(3hat(i)-sqrt(3)hat(j))m//s`
    B
    `(2sqrt(3)hat(i)-2 sqrt(3)hat(j))m//s`
    C
    `(2hat(i)-2 sqrt(3)hat(j))m//s`
    D
    `(sqrt(3)hat(i)-sqrt(3)hat(j))m//s`

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