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 = 10m/s2)

Question

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 = 10m/s2) (A) 10 rad/s (B) 10 π rad/s (C) √10 rad/s (D) (10/2π) rad/s

Tardigrade Admin · Accepted Answer

For equilibrium of the block limiting friction fL ge mg ⇒ μ N ge mg ⇒ μ mrω2 ge mg ω ge √(g/rμ) ωmin =√(g/rμ) ωmin = √(10/0.1 ×1) = 10 rad/s

10 rad/s

10 $π$ rad/s

$10 r a d / s$

$\frac{10}{2 π}$ rad/s

For equilibrium of the block limiting friction
$f_{L} \geq m g$
$\Rightarrow μ N \geq m g$
$\Rightarrow μ m r ω^{2} \geq m g$
$ω \geq \frac{g}{r μ}$
$ω_{min} = \frac{g}{r μ}$
$ω_{min} = \frac{10}{0.1 \times 1} = 10$ rad/s

10 rad/s

10 π rad/s

10​rad/s

2π10​ rad/s

For equilibrium of the block limiting friction fL​≥mg ⇒μN≥mg ⇒μmrω2≥mg ω≥rμg​​ ωmin​=rμg​​ ωmin​=0.1×110​​=10 rad/s

10 $π$ rad/s

$10 r a d / s$

$\frac{10}{2 π}$ rad/s

For equilibrium of the block limiting friction
$f_{L} \geq m g$
$\Rightarrow μ N \geq m g$
$\Rightarrow μ m r ω^{2} \geq m g$
$ω \geq \frac{g}{r μ}$
$ω_{min} = \frac{g}{r μ}$
$ω_{min} = \frac{10}{0.1 \times 1} = 10$ rad/s