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Q.

A disc of mass $5 \times 10^{- 2} kg$ is kept floating horizontally in mid air by firing bullets of mass 0.01kg each vertically at it at the rate of 600 bullets per minute. If the bullets rebound with the same speed, the speed of the bullet striking the disc is $(g = 10 {ms}^{- 2})$

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a

$2 {ms}^{- 1}$

b

$1 {ms}^{- 1}$

c

$5 {ms}^{- 1}$

d

$2.5 {ms}^{- 1}$

answer is C.

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Detailed Solution

For disc in equilibrium

$↑ Force due to bullets striking =↓ wt of disc$

${(\frac{N m Δ V}{t})}_{bullet} = M_{disc} g$

$\frac{600 (10^{- 2}) (2 u)}{60} = 5 \times 10^{- 2} (10)$

$u = 2.5 m / \sec$

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A disc of mass 5×10−2kg is kept floating horizontally in mid air by firing bullets of mass 0.01kg each vertically at it at the rate of 600 bullets per minute. If the bullets rebound with the same speed, the speed of the bullet striking the disc is g=10ms−2