A bullet of mass 0.1 kg moving horizontally with speed 400 hits a wooden block of mass 3.9 kg kept on a horizontal rough surface. The bullet gets embedded into the block and moves 20 m before coming to rest. The coefficient of friction between the block

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Solution

Q.
A bullet of mass 0.1 kg moving horizontally with speed 400 ${ms}^{- 1}$ hits a wooden block of mass 3.9 kg kept on a horizontal rough surface. The bullet gets embedded into the block and moves 20 m before coming to rest. The coefficient of friction between the block and the surface is ______.(Given g = 10 $m / s^{2}$ ) [2023]

1 0.25

2 0.50

3 0.90

4 0.65

Ans.
(1)

$P_{i} = P_{f} (collision)$

$\Rightarrow (0.1) (400) = (0.1 + 3.9) v$

$\Rightarrow v = \frac{0.1 \times 400}{4} = 10 m/s$

$a = \frac{μ m g}{m} = μ g$

$Apply equation of motion, v^{2} = u^{2} + 2 a s$

$\Rightarrow 0^{2} = {(10)}^{2} - 2 μ g \times 20$

$\Rightarrow 40 μ g = 100$

$\Rightarrow μ = \frac{100}{2 \times 10 \times 20} = \frac{1}{4}$

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