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## Homework Statement

Calculate the moment of inertia of a spherical shell (i.e. hollow sphere) of uniform surface density about an axis passing through its center.

## Homework Equations

## The Attempt at a Solution

Integral ( r^2 * dm)

Integral (r^2 * p * dV) ..... where p=density

p * Integral (r^2 * dV)

where V= (4/3)* pi * r^3

and dV= 4 * pi* r^2

therefore,

p * Integral (r^2 *4 * pi* r^2)

4*p*pi* Integral (r^4)

4*p*pi* ((r^5)/5) from 0 to r

p=density=m/V= m/(4/3 * pi * r^3)

4*m/(4/3 * pi * r^3)*pi* ((r^5)/5

(3*m*r^2)/5

but it should be (2*m*r^2)/3.

Please help!