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A uniform rod AB of mass m and length L is tied, at its end B, to a thread which is attached to point P on the ceiling. Length of the thread PB is 0.75 L. The other end A of the rod is hinged at a point on the ceiling. Distance AP = 1.25 L. End B of the rod is pushed gently perpendicular to the plane of the figure and it starts oscillating. Assuming that the triangle APB makes a small angle $θ$ with the vertical plane, write the restoring torque acting on the rod.

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$\frac{3}{7} mgLθ$

$\frac{1}{10} mgLθ$

$\frac{7}{10} mgLθ$

$\frac{3}{10} mgLθ$

answer is C.

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Detailed Solution

$τ = mg \frac{L}{2} \sin θ_{0} \cdot \sin θ ≃ (mg \frac{L}{2} \sin θ_{0}) θ$ [for small $θ$ ]
$= \frac{3}{10} mgLθ$

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