A rectangular lop has mass `M` and sides `a` and `b`. An axis `OO'` passes through the centre `C` of the loop and is parallel to side a (lie in the plane of the loop). Then the radius of gyration of the loop, for the axis `OO'` is.
.

Options

A. `(b)/(2) sqrt((b + 3a)/(3(b + a)))`
B. `sqrt((a^2 + b^2))/(12)`
C. `sqrt((b^2 + 3a^2)/(12))`
D. none of these

Answer

A

Explanation

(a) Let `lamda` is linear mass density.
Mass of side `a` : `m_1 = lamda a`, Mass of side `b` : `m_2 = lamda b`
`I_(O O') = 2[m_1((b)/(2))^2 + (m_2 b^2)/(12)]`
Now,`K_(OO') = sqrt((I_(o o'))/(2(m_1 + m_2)))`.