The moment of inertia of hollow sphee (mass M) of inner radius R and outer radius 2R, having material of uniform density, about a diametric axis isA. `31MR^(2)//70`B. `43MR^(2)//90`C. `19MR^(2)//80`D. None of these

The moment of inertia of hollow sphee (mass M) of inner radius R and o

1.	The moment of inertia of hollow sphee (mass M) of inner radius R and outer radius 2R, having material of uniform density, about a diametric axis isA. `31MR^(2)//70`B. `43MR^(2)//90`C. `19MR^(2)//80`D. None of these
Answer» `rho=(M)/({(4)/(3)pi(2R)^(3)}-{(4)/(3)piR^(3)})` `=(3M)/(28piR^(3))` `M_(2R)=rho((4)/(3))(pi)(2R)^(3)` `=((3)/(28))((4)/(3))(8)M=(8)/(7)M` `M_(R)=rho((4)/(3)piR^(3))` `=((3)/(28))((4)/(3))M=(1)/(7)M` Now, `I=I_(2R)-I_(R)` `=(1)/(2)M_(2R)(2R)^(2)-(1)/(2)M_(R)R^(2)` `=(1)/(2)((8)/(7)M)(4R^(2))-(1)/(2)((M)/(7))R^(2)` `=(31)/(14)MR^(2)`

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The moment of inertia of hollow sphee (mass M) of inner radius R and outer radius 2R, having material of uniform density, about a diametric axis isA. `31MR^(2)//70`B. `43MR^(2)//90`C. `19MR^(2)//80`D. None of these

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