Two solid spheres of the same mass are of steel and aluminium. If `I_(S) and I_(A)` denote their moments of inertia about their diameters, then

Options

A. `I_(S)=I_(A)`
B. `I_(S) gt I_(A)`
C. `I_(S) lt I_(A)`
D. none of the above

Answer

C

Explanation

Mass of a sphere `=v rho =(4)/(3)piR^(3)rho`
`therefore (4)/(3)piR_(A)^(3)rho_(A)=(4)/(3)piR_(S)^(3)rho_(S)`
`therefore" "(R_(A)^(3))/(R_(S)^(3))=(rho_(S))/(rho_(A))" "because rho_("steel")gt rho_(Al)`
`therefore" "R_(A)^(3)gtR_(S)^(3) or R_(A) gt R_(S)`
`"M.I. of the steel sphere "I_(S)=(2)/(5)MR_(S)^(2)`
`"and M.I. of the Al sphere "I_(A)=(2)/(5)MR_(A)^(2)`
`because R_(A)gt R_(S), I_(A)gt I_(S) or I_(S) lt I_(A)`