A uniform rod of mass m and length 'l' is attached to smooth hinge at end A and to a string at end B as shown in figure. It is at rest initially. The angular acceleration of the rod just after the string is cut is:
Answers
The angular acceleration of the rod just after the string is cut is 3g/4l.
explanation : mass of rod = m
length of rod = l
angle made by rod with the horizontal, θ = 60°
centre of mass of rod lies at its midpoint.
so, position of centre of mass from the fixed point, r = (l/2)cos60° = (l/4)
at the instant string is cut, torque = I × α
here I is moment of inertia of rod about an axis passing through one end.
⇒ mg(l/4) = ml²/3 × α
⇒α = 3g/4l
The angular acceleration of the rod just after the string is cut is 3g/4l
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