Question:
A block of mass \(m = 10\ \mathrm{kg}\) rests on a horizontal table. The coefficient of friction between the block and the table is 0.05. When hit by a bullet of mass 50 g moving with speed \(v\), that gets embedded in it, the block moves and comes to stop after moving a distance of 2 m on the table. If a freely falling object were to acquire speed \(\frac{v}{10}\) after being dropped from height \(H\), then neglecting energy losses and taking \(g = 10\ \mathrm{m\,s^{-2}}\), the value of \(H\) is close to
A block of mass \(m = 10\ \mathrm{kg}\) rests on a horizontal table. The coefficient of friction between the block and the table is 0.05. When hit by a bullet of mass 50 g moving with speed \(v\), that gets embedded in it, the block moves and comes to stop after moving a distance of 2 m on the table. If a freely falling object were to acquire speed \(\frac{v}{10}\) after being dropped from height \(H\), then neglecting energy losses and taking \(g = 10\ \mathrm{m\,s^{-2}}\), the value of \(H\) is close to
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Get the speed of block+bullet from work against friction, then v from momentum conservation, then H = (v/10)^2/(2g).
Updated On: Nov 11, 2026
- \(0.2\ \mathrm{km}\)
- \(0.5\ \mathrm{km}\)
- \(0.4\ \mathrm{km}\)
- None of these
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The Correct Option is D
Solution and Explanation
After impact the combined mass is 10.05 kg with speed V; friction work: \(\mu (M+m) g s=\frac12 (M+m)V^2\), so \(V^2=2\mu g s=2(0.05)(10)(2)=2\), \(V=\sqrt2\ \mathrm{m/s}\).
Momentum: \(0.05\,v=10.05\sqrt2\), so \(v=201\sqrt2\approx 284.3\ \mathrm{m/s}\).
Speed of the falling object \(=\frac{v}{10}\approx 28.4\ \mathrm{m/s}\), so \(H=\frac{(v/10)^2}{2g}=\frac{808}{20}\approx 40.4\ \mathrm{m}=0.04\ \mathrm{km}\).
This is not 0.2, 0.5 or 0.4 km.
Answer: (4) None of these
Momentum: \(0.05\,v=10.05\sqrt2\), so \(v=201\sqrt2\approx 284.3\ \mathrm{m/s}\).
Speed of the falling object \(=\frac{v}{10}\approx 28.4\ \mathrm{m/s}\), so \(H=\frac{(v/10)^2}{2g}=\frac{808}{20}\approx 40.4\ \mathrm{m}=0.04\ \mathrm{km}\).
This is not 0.2, 0.5 or 0.4 km.
Answer: (4) None of these
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