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A boy of mass 30 kg starts running from rest along a circular path of radius 6m with constant tangential acceleration of magnitude $2 m / s^{2} .$ After 2 s from start he feels that his shoes started slipping on ground. The friction coefficient between his shoe and ground is $μ .$ Find $6 μ ? (T a k e g = 10 m / s^{2})$

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Detailed Solution

After 2 sec speed of boy will be $v = 2 \times 2 = 4 m / s$

At this moment centripetal force on boy is $F_{r} = \frac{m v^{2}}{R} = \frac{30 \times 16}{6} = 80 N$

Tangential force on boy is $F = \sqrt{F_{r}^{2} + F_{t}^{2}} = 100 N$

At this time of slipping $F = μ m g$ or $100 = μ \times 30 \times 10 \Rightarrow μ = \frac{1}{3}$

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