A sphere P of mass m moving with velocity u collides head on with another sphere Q of mass m which is at rest . The ratio of final velocity of Q to initial velocity of P is ( e = coefficient of restitution )A. `(e - 1)/(2)`B. `[(e+ 1)/(2)]^(1//2)`C. `(e + 1)/(2)`D. `[(e+1)/(2)]^(2)`

A sphere P of mass m moving with velocity u collides head on with anot

1.	A sphere P of mass m moving with velocity u collides head on with another sphere Q of mass m which is at rest . The ratio of final velocity of Q to initial velocity of P is ( e = coefficient of restitution )A. `(e - 1)/(2)`B. `[(e+ 1)/(2)]^(1//2)`C. `(e + 1)/(2)`D. `[(e+1)/(2)]^(2)`
Answer» Correct Answer - C Here , `m_(1) = m_(2) = m , u_(1) = u,u_(2) = 0` Let `v_(1) , v_(2)` be their velocities after collision According to principle of conservation of linear momentum mu + 0 = `m(v_(1) + v_(2))` or `v_(1) + v_(2) = v " " … (i)` By definition , `e = (v_(2) - v_(1))/(u - 0) ` or `v_(2) - v_(1) = eu " " ... (ii)` Adding Eqs. (i) and (ii) , we get `v_(2) = (u (1 + e))/(2) implies (v_(2))/(u) = (1 + e)/(2)`

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A sphere P of mass m moving with velocity u collides head on with another sphere Q of mass m which is at rest . The ratio of final velocity of Q to initial velocity of P is ( e = coefficient of restitution )A. `(e - 1)/(2)`B. `[(e+ 1)/(2)]^(1//2)`C. `(e + 1)/(2)`D. `[(e+1)/(2)]^(2)`

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