First slide

Torque

Question

A thin rod AB of mass m and Length ‘l' is lying on a frictionless horizontal surface. Two forces, each of magnitude F are applied to the rod at points A and M. Then select the correct option.

Moderate

A

Acceleration of centre of mass is $\frac{F}{m}$
B

Angular acceleration of the rod is $\frac{9 F}{ml}$
C

Acceleration of centre of mass is $\frac{F}{2 m}$
D

The rod is not in transnational equilibrium

Solution

Net force on the rod = F - F = 0. So acceleration of centre of mass is zero and the rod is transnational equilibrium.
Resultant torque about the centre of mass C
$= F . \frac{l}{2} + F . \frac{l}{4} = \frac{3 Fl}{4} .$
Moment of inertia of the rod about an axis perpendicular to the rod passing through the centre of mass $I_{C} = \frac{1}{12} {ml}^{2}$
$∴$ Angular acceleration $α = \frac{τ}{I_{C}} = \frac{3 Fl}{4} \times \frac{12}{{ml}^{2}} = \frac{9 F}{ml}$

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