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A bullet of mass 10g and speed $500 m s^{- 1}$ is fired into a door and gets embedded exactly at the centre of the door. The door is 2 m wide and weighs 12 kg. It is hinzed at one end and rotates about a vertical axis without friction. The angular speed of door just after the bullet embeds into it is.

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$\frac{5}{8} r a d s^{- 1}$

$\frac{5}{16} r a d s^{- 1}$

$\frac{5}{4} r a d s^{- 1}$

$\frac{5}{32} r a d s^{- 1}$

answer is B.

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Detailed Solution

$m V L = I ω$
$10 \times 10^{- 3} \times 500 \times 1 = \frac{12 \times 2^{2}}{3} . ω$

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