Two sphere each of mass M and radius R/2 are connected with a massless rod of length 2 R as shown in the moment of inertia of the system about an axis passing through the centre of one of the sphere and perpendicular to the rod ?

Options

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

Answer

A

Explanation

Moment of nertia of the system about YY'
`l_("YY'")`=Moment of inertia of sphere P about YY'
`+` Moment of inertia of sphere Q about YY,
Moment of inertia of sphere P about YY'
`=(2)/(5)M((R)/(2))^(2)+M(x)^(2)`
`=(2)/(5)M((R)/(2))^(2)+M(2R)^(2)`
`=(MR^(2))/(10)+4MR^(2)`
Moment of inertia of sphere Q about YY' is `(2)/(5)M((R)/(2))^(2)`
Now,`" "l_("YY'")=(MR^(2))/(10)+4MR^(2)+(2)/(5)M((R)/(2))^(2)=(21)/(5)MR^(2)`