Two blocks tied with a mass less string of length 3m are placed on a rotating table as shown. The axis of rotation is 1m from 1kg mass and 2m from 2 kg mass. If coefficient of friction between 2kg block and ground is $μ = 0 .$ and that of between 1kg block and ground is $μ = 0.8$ The maximum angular speed so that neither of the blocks slips is_________.
$(g = 10 m / s^{2})$

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$4 rad/s$

$3.26 rad/s$

$5 rad/s$

$1.63 rad/s$

answer is B.

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Detailed Solution

$f_{\max} = μ m_{1} g = 0.8 \times 1 \times 10 = 8 N$

$T = m_{2} r_{2} ω^{2} = (2) (2) ω^{2} = 4 ω^{2} \dots . . (i)$

$T - 8 = m_{1} r_{1} ω^{2} = (1) (1) (ω^{2}) = ω^{2} \dots . . (i i)$

Solving Eqs. (i) and (ii) we get, $ω = 1.63 r a d / s$

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