In the adjacent figure ABC is a uniform isosceles triangular lamina of mass m and `AB=AC=l` the lamina is free to rotate about a fixed horizontal axis `OAO^(')` which is in the plane of the lamina. Initially the lamina is in static equilibrium with maximum gravitational potential energy. due to slight disturbance, lamina starts rotating. Now choose the correct option(s)

Options

A. The maximum angular speed acquried by lamina is `4sqrt((sqrt(2)g)/(3l))`
B. The maximum vertical force on the axis by the lamina is `(41)/(9)mg`
C. Angular momentum of the lamina about `OAO^(')` is conserved
D. When the lamina acquire maximum angular speed acceleration of centre of mass is zero.

Answer

A, B

Explanation

`because-DeltaU=DeltaK`
`(2sqrt(2)mgl)/(3)=(1)/(2).(ml^(2)omega^(2))/(4)`
(moment of inertial about `OAO^(')=(ml^(2))/(4))`
`impliesomega=sqrt((16sqrt(2))/(3).(g)/(l))=4sqrt((sqrt(2)g)/(3l))`
`becauseF-mg=momega^(2)R=mxx(16sqrt(2)g)/(3l).(sqrt(2)l)/(3)`
`impliesF=mg+(32mg)/(9)=(41mg)/(9)`