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One-fourth length of a uniform rod is placed on a rough horizontal surface and it starts rotating about the edge as soon as we release it. The rod starts slipping on the edge when it has turned through an angle θ . If the coefficient of friction between rod and surface is μ , and it satisfies the relation x tan θ = 4 μ , then what is the value of x ? [Take g = 10 m / s 2 ]

Correct answer

13

Step-by-step solution

m g l 4 sin ⁡ θ = 1 2 I ω 2 α = m g l 4 cos ⁡ θ I μ N - m g sin ⁡ θ = m ω 2 l 4 m g cos ⁡ θ - N = m l 4 α Solving, 13 tan ⁡ θ = 4 μ .

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