MHT CET · Physics · Center of Mass Momentum and Collision
A ball kept at \(20 \mathrm{~m}\) height falls freely in downward direction vertically and hits the ground. The coefficient of restitution is \(0.4 .\) After the first rebound the upward
velocity is \(\left[\mathrm{g}=10 \mathrm{~m} / \mathrm{s}^{2}\right]\)
- A \(8 \mathrm{~m} / \mathrm{s}\)
- B \(12 \mathrm{~m} / \mathrm{s}\)
- C \(4 \mathrm{~m} / \mathrm{s}\)
- D \(16 \mathrm{~m} / \mathrm{s}\)
Answer & Solution
Correct Answer
(A) \(8 \mathrm{~m} / \mathrm{s}\)
Step-by-step Solution
Detailed explanation
\(8 \mathrm{~m} / \mathrm{s}\)
\(h=20 \mathrm{~m}, \mathrm{e}=0.4 \mathrm{~m}\)
\(\therefore v^{2}=0+2 g h=2 \times 10 \times 20\)
\(\therefore v=2 \times 10=20\)
\(e=\frac{\mathrm{u}}{\mathrm{v}}\)
\(\therefore \mathrm{u}=\mathrm{ev}=0.4 \times 20=8 \mathrm{~m} / \mathrm{s}\)
\(h=20 \mathrm{~m}, \mathrm{e}=0.4 \mathrm{~m}\)
\(\therefore v^{2}=0+2 g h=2 \times 10 \times 20\)
\(\therefore v=2 \times 10=20\)
\(e=\frac{\mathrm{u}}{\mathrm{v}}\)
\(\therefore \mathrm{u}=\mathrm{ev}=0.4 \times 20=8 \mathrm{~m} / \mathrm{s}\)
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