Question

The surface density (mass/area) of a circular disc of radius a depends on the distance from the centre as `rho(r)=A+Br.` Find its moment of inertia about the line perpendicular to the plane of the disc through its centre.
A. `pia^(2)(A/2 + (2a)/5)`B
B. `pia^(4)(A/2 + (2B)/5)`
C. `2pia^(3)(A/2+ (Ba)/5)`
D. None of these

Answer 1

a) dm = `2pirdr(rho)` = (A+Br)(2pirdr)`
`I = int_(0)^(a)dmr^(2)` = `(piAa^(4))/2+ (2piBa^(5))/5 = pia^(4)(A/2+(2a)/5B)`