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Q.

A disc of mass $m 1$ radius r is released from rest in the fig shown. If the cylinder is on the verge of slipping as well as toppling then coefficient of friction between cylinder and table surface is:

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a

1

b

12

c

3

d

13

answer is A.

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Detailed Solution

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$m 1 g − T = m 1 a$
$T r = m_{1} \frac{r^{2}}{2} \frac{a}{r} \Rightarrow a = \frac{2 g}{3}; T = \frac{m_{1} g}{3}$
Also, $T = μ m 2 g, ⇒ μ = m 1 3 m 2$
Balancing torque about the edge, we get $T R = m 2 g R$
$\Rightarrow \frac{m_{1} g}{3} \times R = m_{2} g R \Rightarrow m_{1} = 3 m_{2} \Rightarrow μ = \frac{m_{1}}{3 m_{2}} = 1$

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