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  4. A bullet of mass 10 g moving horizontally with a velocity of 400 m s- 1 strikes a wooden block of mass 2 kg which is suspended by a light inextensible string of length 5 m. As a result, the centre of gravity of the block is found to rise a vertical distance of 10 cm. The speed of the bullet after it emerges out horizontally from the block will be

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Q. A bullet of mass $10 g$ moving horizontally with a velocity of $400 \, m \, s^{- 1}$ strikes a wooden block of mass $2 kg$ which is suspended by a light inextensible string of length $5 m.$ As a result, the centre of gravity of the block is found to rise a vertical distance of $10 cm.$ The speed of the bullet after it emerges out horizontally from the block will be

NTA AbhyasNTA Abhyas 2020

Solution:

CM rises through height h, so its velocity after collision $=\sqrt{2 g h}$
Apply conservation of linear momentum.
$0.01\times 400=2\times \sqrt{2 g h}+0.01\times v$
$\Rightarrow v=120 \, m/s$