Question

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

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

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

Answer 1

Answer: (B)

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