Mass per unit area of a circular disc of radius a depends on the distance $r$ from its centre as $\sigma ( r ) = A + B r$. The moment of inertia of the disc about the axis, perpendicular to the plane and passing through its centre is: (1) $2 \pi a ^ { 4 } \left( \frac { A } { 4 } + \frac { a B } { 5 } \right)$ (2) $2 \pi a ^ { 4 } \left( \frac { a A } { 4 } + \frac { B } { 5 } \right)$ (3) $\pi a ^ { 4 } \left( \frac { A } { 4 } + \frac { a B } { 5 } \right)$ (4) $2 \pi \mathrm { a } ^ { 4 } \left( \frac { \mathrm {~A} } { 4 } + \frac { \mathrm { B } } { 5 } \right)$
Mass per unit area of a circular disc of radius a depends on the distance $r$ from its centre as $\sigma ( r ) = A + B r$. The moment of inertia of the disc about the axis, perpendicular to the plane and passing through its centre is:\\
(1) $2 \pi a ^ { 4 } \left( \frac { A } { 4 } + \frac { a B } { 5 } \right)$\\
(2) $2 \pi a ^ { 4 } \left( \frac { a A } { 4 } + \frac { B } { 5 } \right)$\\
(3) $\pi a ^ { 4 } \left( \frac { A } { 4 } + \frac { a B } { 5 } \right)$\\
(4) $2 \pi \mathrm { a } ^ { 4 } \left( \frac { \mathrm {~A} } { 4 } + \frac { \mathrm { B } } { 5 } \right)$