One solid sphere $A$ and another hollow sphere $B$ are of same mass and same outer radii, Their moments of…

One solid sphere $A$ and another hollow sphere $B$ are of same mass and same outer radii, Their moments of inertia about their diameters are respectively $I_{A}$ and $I_{B}$, such that
  1. \(\mathrm{I}_{\mathrm{A}}=\mathrm{I}_{\mathrm{B}}\)
  2. \(\mathrm{I}_{\mathrm{A}}>\mathrm{I}_{\mathrm{B}}\)
  3. \(\mathrm{I}_{\mathrm{A}}<\mathrm{I}_{\mathrm{B}}\)
  4. \(\mathrm{I}_{\mathrm{A}} / \mathrm{I}_{\mathrm{B}}=\mathrm{d}_{\mathrm{A}} / \mathrm{d}_{\mathrm{B}}\)

Solution

Given; mass and radius of both the spheres are same. Now as moment of inertia of solid sphere, \(\mathrm{I}_{\mathrm{A}}=\frac{2}{5} \mathrm{MR}^{2}\) Moment of inertia of hollow sphere, \(\mathrm{I}_{\mathrm{B}}=\frac{2}{3} \mathrm{MR}^{2}\) \(\Longrightarrow \mathrm{I}_{\mathrm{A}}<\mathrm{I}_{\mathrm{B}}\)

Asked in: JEE Mains - Rotational Motion - Test 1

Practice more Rotational Motion questions on Aicharya