MHT CET · Physics · Center of Mass Momentum and Collision
A sphere of mass 'm', moving with velocity '3u' collides head-on with another identical sphere at rest. If ' e ' is coefficient of restitution then what will be the ratio of velocity of the second sphere to that of first sphere after collision?
- A \(\frac{1-\mathrm{e}}{1+\mathrm{e}}\)
- B \(\frac{1+e}{1-e}\)
- C \(\frac{\mathrm{e}+1}{\mathrm{e}-1}\)
- D \(\frac{e-1}{e+1}\)
Answer & Solution
Correct Answer
(B) \(\frac{1+e}{1-e}\)
Step-by-step Solution
Detailed explanation
\(m u_1 + m u_2 = m v_1 + m v_2 \Rightarrow 3u + 0 = v_1 + v_2 \Rightarrow v_1 + v_2 = 3u\) (1) \(e = \frac{v_2 - v_1}{u_1 - u_2} \Rightarrow e = \frac{v_2 - v_1}{3u - 0} \Rightarrow v_2 - v_1 = 3eu\) (2)
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