A rod PQ of mass M and length L is hinged at end P. The rod is kept horizontal by a massless string tied to point Q as shown in figure. When string is cut, the initial angular acceleration of the rod is

Question

A rod PQ of mass M and length L is hinged at end P. The rod is kept horizontal by a massless string tied to point Q as shown in figure. When string is cut, the initial angular acceleration of the rod is

Infinity Learn · Accepted Answer

When the string is cut, the rod will rotate about P. Let α be initial angular acceleration of the rod. ThenTorque, τ$$=I$$α$$=ML23$$α        −−−(i) $$($$ ∵ Moment of inertia of the rod about one end $$=ML23$$ $$)$$ Also, τ$$=MgL2$$          −−−(ii) Equating (i) and (ii), we get $$MgL2=ML23$$α   or  α$$=3g2L$$

A rod PQ of mass M and length L is hinged at end P. The rod is kept horizontal by a massless string tied to point Q as shown in figure. When string is cut, the initial angular acceleration of the rod is

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