TS EAMCET · Physics · Center of Mass Momentum and Collision
A body of mass ' \(m\) ' moving with a velocity of ' \(v\) ' collides head on with another body of mass ' 2 m ' at rest. If the coefficient of restitution between the two bodies is ' e ', then the ratio of the velocities of the two bodies after collision is
- A \(\frac{1+\mathrm{e}}{1-2 \mathrm{e}}\)
- B \(\frac{1+2 \mathrm{e}}{1-\mathrm{e}}\)
- C \(\frac{1-\mathrm{e}}{1+2 \mathrm{e}}\)
- D \(\frac{1-2 \mathrm{e}}{1+\mathrm{e}}\)
Answer & Solution
Correct Answer
(D) \(\frac{1-2 \mathrm{e}}{1+\mathrm{e}}\)
Step-by-step Solution
Detailed explanation
\(m u_1 + 2m u_2 = m v_1 + 2m v_2\) \(m v + 2m (0) = m v_1 + 2m v_2\) \(v = v_1 + 2 v_2\) (1) \(e = \frac{v_2 - v_1}{u_1 - u_2}\) \(e = \frac{v_2 - v_1}{v - 0}\) \(e v = v_2 - v_1\) (2) Substitute \(v_1 = v_2 - e v\) from (2) into (1): \(v = (v_2 - e v) + 2 v_2\)…
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