Question

If the temperature of metal sphere increases by △t , the fractional change in its moment of inertia is (α=Coefficientoflinearexpansion)

Answer 1

If the temperature of metal sphere increases by △t , the fractional change in its moment of inertia is formulated as;

I₀ =25*m*r₀²

I′ =25*m*[r₀²(1+α*△t)*2]

I′ =25*m*r₀²[1+2*α*△t]

△I= 25*m*r₀²(2*α*△t)

△I/I₀ =2α△t

where, △I/I₀= fractional change

m = mass of metal sphere

r = radius of metal sphere

α=Coefficient of linear expansion