A thin uniform rod of mass 1 kg and length 12 cm is suspended by a wire that passes through its centre and is perpendicular to its length.The wire is twisted and the rod is set oscillating. Time period of oscillation is found to be 3 s. When a flat triangular plate is suspended in same way through its centre of mass, the time period is found to be 6 s. The moment of inertia of the tringular plate about this axis is

Options

A. `0.12kg-m^2`
B. `0.24kg-m^2`
C. `0.48kg-m^2`
D. information insufficient

Answer

C

Explanation

For torsional pendulum time period is given by
`T=2pisqrt((I)/(k))`
where `k` is torsional constant of string and it is same for both the cases.
`I_(rod)=(mL^2)/(12)=(1xx1.2^2)/(12)=0.12kg-m^2`
`(T_(rod))/(T_(plate))=((I_(rod))/(I_(plate)))^((1)/(2))implies((3)/(6))^2=(0.12)/(I_(plate))`
`I_(plate)=0.48kg-m^2`