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

Options

A. `(3g)/(2L)`
B. `(g)/(L)`
C. `(2g)/(L)`
D. `(2g)/(3L)`

Answer

A

Explanation

Torque on the rod = Moment of weight of the rod about P
`tau =mg(L)/(2)" …(i)"`
`because" Moment of inertia of rod arbout,"`
`P=(ML^(2))/(3)" ...(ii)"`
`"As "tau=l alpha`
From Eqs. (i) and (ii), we get
`Mg(L)/(2)=(ML^(2))/(3) alpha rArr alpha=(3g)/(2L)`