A bullet of mass 0.1 kg moving horizontally with speed 400 m s⁻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 i $s _______.$ (Given g = 10 m s⁻²)
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Question

A bullet of mass 0.1 kg moving horizontally with speed 400 m s⁻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 i $s _______.$ (Given g = 10 m s⁻²)

Options

G1 Physics · Accepted Answer

First use momentum conservation during the perfectly inelastic collision. Bullet mass: m = 0.1 kg Block mass: M = 3.9 kg Initial bullet speed: u = 400 m s⁻¹ If common speed just after collision is V: μ \mu μ = (m+M) V 0 .1 × 400 V_0.1×400 V 0 ​ .1 × 400 = 4.0V V = 10 m s⁻¹ Now the combined body stops after sliding 20 m. Using v² = u² + 2as 0 = 10² - 2(μg)(20) 100 = 400μ μ = 0.25 Hence option C follows.