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. What is the distance from axis about which a uniform, balsa-wood sphere will have the same moment of inertia as does a thin-walled, hollow, lead sphere of the same mass and radius R, with the axis along a diameter, to the center of the balsa-wood sphere?

Verified Answer :

Parallel axis thm says that about a point of rotation not the center of mass a distance d away from the center of mass

I=Icm+Md^2

For a hollow lead sphere
IH=2/3MR^2


and the moment of inertia about the center of mass for the balsa sphere is

Icm=2/5MR^2


So to set them equal to each other

IH=Icm+Md^2


2/3MR^2=2/5MR^2+Md^2

M(2/3R^2)=M(2/5R^2+d^2)

cancel out the M

d^2=(2/3−2/5)R^2

answer is \(\sqrt{4/15}\)


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