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NEET 2019 · Two-Body Friction

Two-Body Friction question from NEET 2019

Q9NEET 2019Medium

Two-Body Friction

A block of mass 10 kg is in contact against the inner wall of a hollow cylindrical drum of radius 1 m. The coefficient of friction between the block and the inner wall of the cylinder is 0.1. The minimum angular velocity needed for the cylinder to keep the block stationary when the cylinder is vertical and rotating about its axis, will be: (g = 10 m/s2)

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Answer: (b)

Wall provides normal force $N = m\omega^2 R$ ; friction must hold the weight: $\mu m\omega^2 R \ge mg$ .
$\omega_{min} = \sqrt{\frac{g}{\mu R}} = \sqrt{\frac{10}{0.1 \times 1}}$
$\omega_{min} = 10$ rad/s, so the answer is (b).

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