On a disc of radius R a concentric circle of radius R/2 is drawn. The disc is free to rotate about a frictionless axis through its centre and perpendicular to plane of the disc. All the three forces (

Question

On a disc of radius R a concentric circle of radius R/2 is drawn. The disc is free to rotate about a frictionless axis through its centre and perpendicular to plane of the disc. All the three forces (in plane of the disc) shown in figure act tangentially to their respective circular peripheries. The magnitude of the net torque (about centre of disc) acting on the disc is :-

TestHub · Accepted Answer

Torque of each force about the centre = force × radius of its circle

Force F on the inner circle: $F \cdot \frac{R}{2}$

Force 2F on the outer circle: $2 F \cdot R$

Force F on the outer circle, opposite sense: $- F \cdot R$

$τ = \frac{FR}{2} + 2 FR - FR$

$τ = \frac{3 FR}{2} = 1.5 FR$

Answer: D

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