Question

Let the moment of inertia of a hollow cylinder of length $30\, cm$ (inner radius $10\, cm$ and outer radius $20\, cm$), about its axis be 1. The radius of a thin cylinder of the same mass such that its moment of inertia about its axis is also $I$, is:

• A. 12 cm
• B. 18 cm
• C. 16 cm
• D. 14 cm

Answer 1

The Correct Option is C

The correct answer is (C) : 16
Moment of inertia of hollow cylinder about its axis is given as:
\(I_1=\frac{M}{2}(R^{2}_1+R_{2}^2)\)
Where,
\(R_1\)= Inner radius and \(R_2\)= Outer radius
Moment of inertia of thin hollow cylinder of radius R about its axis is given as:
\(I_2=MR^2\)
Given that
\(I_1=I_2\)
\(⇒\frac{M}{2}(R^{2}_{1}+R^{2}_2)=MR^2\)
Both cylinders have same mass (M)
\(⇒\frac{(R^{2}_1+R^{2}_2)}{2}=R^2\)
\(⇒\frac{(10^2+20^2)}{2}=R^2\)
\(⇒R^2=250=15.8\)
\(∴R≈16 cm\)