Physics Question on Moment Of Inertia

Question

The moment of inertia of a thin rod about an axis passing through its mid point and perpendicular to the rod is 2400 g cm2. The length of the 400 g rod is nearly :

Answer 1

Solution

The moment of inertia of a rod is given by:

$I = \frac{1}{12}ML^2$ .

Here, $I = 2400 \, g cm^2 = 2400 \times 10^{-7} \, kg m^2$ , $M = 400 \, g = 0.4 \, kg$ .

Rearrange to find $L$ :

$L = \sqrt{\frac{12I}{M}} = \sqrt{\frac{12 \times 2400 \times 10^{-7}}{0.4}} = 8.5 \, cm$ .