Find the moment of inertia of a hemisphere of mass `M` and radius `R` shown in the figure, about an axis `A A'` tangential to the hemisphere.

Options

A. `I=(9/20)mR^(2)`
B. `I=(13/20)mR^(2)`
C. `I=(7/20)mR^(2)`
D. `I=(3/20)mR^(2)`

Answer

B

Explanation

Moment of inertia about an axis through the flat face of hemisphere

`I_(0)=2/5 mR^(2)`
From the parallel axis theoram, the moment of inertial through c.m. of the hemisphere
`I_(0)=I_(0)-m(3/8R)^(2)=(83/320)mR^(2)`
Using parallel axis theoram, moment of inertia about the axis `A A'`,
`I=I_(G)+m(5/8R)^(2)rArrI=(13/20)mR^(2)`