A semicircular disc of mass M and radius R is free to rotate about its diameter. The moment of inertia of semicircular disc about a line perpendicular to its plane through centre is

Question

Aicharya · Accepted Answer

The moment of inertia of disc of radius $R$ about its axis is

$I = \frac{M^{'} R^{2}}{2}$

where, $M^{'} =$ mass of complete disc $= 2 M$

$I = \frac{2 M R^{2}}{2}$

$I = M R^{2} . . . (i)$

If $I_{1}$ be the moment of inertia of semicircular disc about its. axis, then disc may be assumed as combination of two semi-circular parts,

Thus, $I = I_{1} + I_{1} \Rightarrow I_{1} = \frac{I}{2} = \frac{M R^{2}}{2}$

A semicircular disc of mass M and radius R is free to rotate about its diameter. The moment of inertia of…

Solution