A ring of mass M and radius R lies in x $$-y$$ plane with its center at origin as shown. The mass distribution of ring is $$non-uniform$$ such that at any point P on the ring, the mass per unit length is given by λ$$=$$λ$$0cos2$$θ where λ$$0$$ is a positive $$constant)$$. Then the moment of inertia of the ring about z axis is

Question

A ring of mass M and radius R lies in x $$-y$$ plane with its center at origin as shown. The mass distribution of ring is $$non-uniform$$ such that at any point P on the ring, the mass per unit length is given by λ$$=$$λ$$0cos2$$θ where λ$$0$$ is a positive $$constant)$$. Then the moment of inertia of the ring about z axis is

Infinity Learn · Accepted Answer

Divide the ring into infinitely small lengths of mass $$dm1$$ . Even though mass distribution is $$non-uniform$$,  each mass $$dm1$$ is at same distance R from origin. ∴ MI of ring about $$z-axis$$ is $$=dm1R2+dm2R2+$$…………..$$+dmnR2=MR2$$

Remember concepts with our Masterclasses.

Ready to Test Your Skills?

free study material