A rod PQ of mass m and length L is hinged at its one end P. The rod is kept horizontal by a massless string tied to end Q. When the string is cut, initial angular acceleration of the rod is
A
3g2L
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B
gL
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C
2gL
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D
2g3L
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Solution
The correct option is A3g2L When string is cut, the rod will rotate about hinge point P.
Let the initial angular acceleration be α.
Let Nx&Ny be the hinge forces but they pass through point P, hence their torques about P vanish.
Applying the equation of torque about P, ∑τ=Iα ⇒τmg=Iα...(i)
From parallel axis theorem, the MOI of the rod about P, I=mL212+mL24
Substituting in Eq.(i), L2×mg=(mL212+mL24)α ⇒mgL2=mL23α ∴α=3g2L
Initial angular acceleration of the rod about P is 3g2L