Two identacal rods each of length `l` and mass `m` weided toeather at right angle and edge suspended from a kinetic sides as shown Angular frequency of small oscillation of the system in its then plane about the total of suspension is

Options

A. `sqrt((3g)/(4sqrt(2)l))`
B. `sqrt((3g)/(2sqrt(2)l))`
C. `sqrt((3g)/(sqrt(2)l))`
D. None of these

Answer

B

Explanation

`C` is combined center of mass

` h = (1)/(2) cos 45^(@) = (1)/(2sqrt(2))`
moments of ineetia of rods about `O : 1 = (2ml^(2))/(3)`
`T = 2pi sqrt((1)/(2mgh))`
` 2pi = sqrt(2ml^(2)sqrt(2))/(3[2mg]l) = 2pi sqrt((2sqrt(2l))/(3g))`
Angular frequancy omega `= (2pi)/(T) = sqrt((3g)/(2sqrt(2l)))`