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  4. The mass m moves in a circular arc of angular amplitude 60° . The minimum coefficient of friction between 4m and surface of table to prevent slipping is, <img class=img-fluid question-image alt=Question src=https://cdn.tardigrade.in/q/nta/p-zmsxcubgw8oss6eg.jpg />

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Q. The mass $m$ moves in a circular arc of angular amplitude $60^\circ $ . The minimum coefficient of friction between $4m$ and surface of table to prevent slipping is,
Question

NTA AbhyasNTA Abhyas 2022

Solution:

For $60^\circ $ circular arc,
$mg\left(\ell - \ell cos 60 ^\circ \right)=\frac{1}{2}mv_{max}^{2}$
$mg=\frac{m v_{max}^{2}}{\ell }$ ...(i)
Solution
Maximum tension in the rope $=mg+\frac{m v_{max}^{2}}{\ell }=2mg$ .
For minimum friction coefficient,
$\mu 4mg=2mg$
$\mu =0.5$