Question

Four balls each of radius $ 10\, cm $ and mass $ 1\, kg, 2\, kg, 3\, kg $ and $ 4 \,kg $ are attached to the periphery of massless plate of radius $ 1\,m $ .

What is moment of inertia of the system about the centre of plate ?

• A. $ 12.04\,kg-m^2 $
• B. $ 10.04 \,kg-m^2 $
• C. $ 11.50 \,kg-m^2 $
• D. $ 5.04 \,kg-m^2 $

Answer 1

Answer: (B)

Moment of inertia of the system about the centre of plate is given by
$I=\left[\frac{2}{5} \times 1 \times(0.1)^{2}+1 \times(1)^{2}\right]$
$+\left[\frac{2}{5} \times 2 \times(0.1)^{2}+2 \times(1)^{2}\right] $
$+\left[\frac{2}{5} \times 3 \times(0.1)^{2}+3 \times(1)^{2}\right] $
$+\left[\frac{2}{5} \times 4 \times(0.1)^{2}+4 \times(1)^{2}\right] $
$= 1.004+2.008+3.012+4.016$
$=10.04\, kg - m ^{2} $