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  4. A rough platform OA rotates in a vertical plane about a horizontal axis through the point O with a constant counterclockwise velocity ω =3 rad s- 1 . As it passes through the position θ =0 , a small mass m is placed upon it at a radial distance. If the mass is observed to slip at θ =37° , then the coefficient of friction between the mass the member is ( consider r=0.5 m and g=10 m s- 2 ) <img class=img-fluid question-image alt=Question src=https://cdn.tardigrade.in/q/nta/p-klipjfg0fqlhdyvj.jpg />

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Q. A rough platform $OA$ rotates in a vertical plane about a horizontal axis through the point $O$ with a constant counterclockwise velocity $\omega =3 \, rad \, s^{- 1}$ . As it passes through the position $\theta =0$ , a small mass $m$ is placed upon it at a radial distance. If the mass is observed to slip at $\theta =37^\circ $ , then the coefficient of friction between the mass & the member is ( consider $r=0.5 \, m$ and $g=10 \, m \, s^{- 2}$ )

Question

NTA AbhyasNTA Abhyas 2022

Solution:

As the mass is at the verge of slipping
$\therefore mg\sin 37-\mu \, mg\cos ⁡ 37=m\ omega ^{2}r$
$6-8 \mu =4.5$
$\therefore \mu =\frac{3}{16}$