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

Answer: (C)

16 cm

Answer 2

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)
$⇒\frac{(R^{2}_1+R^{2}_2)}{2}=R^2$
$⇒\frac{(10^2+20^2)}{2}=R^2$
$⇒R^2=250=15.8$
$∴R≈16 cm$