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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?

2gL

3g2L

gL

2g3L

Solution:

After the string is cut the initial angular acceleration of the rod is generated by torque at Q.
On balancing torque about the Q point
MgL/2 = ML²/3α
α = 3g/2L
Therefore the acceleration of rod is α = 3g/2L