A sphere of mass m moving with a constant velocity u hits another stationary sphere of the same mass. If e is the coefficient of restitution, then the ratio of the velocity of two spheres after collision will be

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Solution

The correct option is A

$L e t t h e f i n a l v e l o c i t i e s o f t h e t w o m a s s e s b e v_{1} a n d v_{2} B y d e f i n i t i o n, e = \frac{v_{2} - v_{1}}{0 - 4} C o n s e r v a t i o n o f l i n e a r m o m e n t u m, m (u) + 0 = m v_{1} + m v_{2} \Rightarrow v_{1} + v_{2} = 4 ∴ \frac{v_{1} + v_{2}}{v_{2} - v_{1}} = \frac{4}{- e 4} \frac{v_{1} + v_{2}}{v_{1} - v_{2}} = \frac{1}{e} ∴ \frac{v_{1}}{v_{2}} = \frac{1 + e}{1 - e} \frac{v_{2}}{v_{1}} = \frac{1 - e}{1 + e}$

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A sphere of mass m moving with a constant velocity u hits another stationary sphere of the same mass. If e is the coefficient of restitution, then the ratio of the velocity of two spheres after collision will be

The correct option is A Let the final velocities of the two masses be v1 and v2 By definition, e=v2−v10−4Conservation of linear momentum, m(u)+0=mv1+mv2⇒v1+v2=4∴v1+v2v2−v1=4−e4v1+v2v1−v2=1e∴v1v2=1+e1−ev2v1=1−e1+e