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Questions  

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  [NEET 2013)

a
3g2L
b
gL
c
2gL
d
2g3L

detailed solution

Correct option is A

When the string is cut, the rod can be shown asTorque on the rod = Moment of weight of the rod about P,τ=MgL2               …(i)∵  Moment of inertia of rod about  P,I=ML23      . ..(ii)As,   τ=IαFrom Eqs. (i) and (ii), we getMgL2=ML23α∴   The initial angular acceleration of the rod,  α=3g2L

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