A uniform pole of length l and mass m is pivoted on the ground with a frictionless hinge O. The pole is free to rotate without friction about an horizontal axis axis passing through O and normal to plane of the page. The pole makes an angle θ with the horizontal. The pole is released from rest in the position shown, then linear acceleration of the free end (P) of the pole just after its release would be
Solution:
Torque of gravitational force mg about O is mgcosθ ×L/2
Torque = I × α
mgcosθ ×L/2 = (mL²/3) × α
α = (3gcosθ)/2