A square plate of mass M and side length L is hinged at one of its vertex (A) and is free to rotate about it. Find the time period of small oscillations if
(a) the plate performs oscillations in the vertical plane of the figure. (Axis is perpendicular to figure.)
(b) the plate performs oscillations about a horizontal axis passing through A lying in the plane of the figure.

Options

A. `2pi sqrt((2a)/(3g))`
B. `2 pi sqrt((sqrt(2)a)/(3g))`
C. `2pisqrt((2sqrt(2)a)/(3g))`
D. `2 pi sqrt((2sqrt(2a))/(g))`

Answer

C

Explanation

`T = 2pi sqrt((1)/(mgd)) = 2pi sqrt((m((a^(2) + a^(2)))/(12) + m((a)/(sqrt(2)))^(2))/(mg"(a)/(sqrt(2))))`
`= 2pi sqrt(((a)/(6) + (a)/(2)) .sqrt(2))/(g) = 2pi sqrt(2sqrt(2)a)/(3g)`