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A particle of mass m strikes elastically...

A particle of mass `m` strikes elastically with a disc of radius `R`, with a velocity `vec"v"` as shown in the figure. If the mass of the disc is equal to that of the particle and the surface of the contact is smooth, find the velocity of the disc just after the collision.

Text Solution

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We see that impact takes place along the normal. Therefore, the particle and the disc change their momentum along that line. However, no external force acts on the system along the norma line. Hence we can conserve the linear momentum of the system (disc+particle) along the normal. Since the masses of the disc and particle are equal, so the exchange of momentum takes place along the normal. That means, the particle completely delivers the part (component) of its momentum `("m v"costheta)` along the normal

`rArr` Velocity of the disc, `vecvv_(1)=(vcostheta)hatj` where, `costheta=cos30^(@)=(sqrt3)/(2)`
`rArr" "vecv_(1)=(sqrt3v)/(2)hatj`
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