Two spheres each of mass M and radius `(R )/(2)` are connected with a massless rod of length 2R as shown in the figure.

The moment fo inertia of the system about an axis passing through the centre of one of the spheres and perpendicular to the rod about yy' axis will be :

Options

A. `(21)/(5)MR^(2)`
B. `(2)/(5)MR^(2)`
C. `(5)/(2)MR^(2)`
D. `(5)/(21)MR^(2)`

Answer

A

Explanation

`I_(yy)=(2)/(5)M((R)/(2))^(2)+(2)/(5)M((R)/(2))^(2)+M(2R)^(2)`
`I_(yy)=(MR^(2))/(10)+(MR^(2))/(10)+4MR^(2)=(MR^(2))/(5)+4MR^(2)`
`I_(yy)=((21MR^(2))/(5))`