Question

A system of five solid spheres each of mass '\(m\)' and radius '\(r\)' are rotating about an axis AA' as shown in figure. Hence the moment of inertia of the system about the axis of rotation AA' is

• A. \(6 mr^2\)
• B. \(5 mr^2\)
• C. \(4 mr^2\)
• D. \(3 mr^2\)

Hint:

Spheres on the axis contribute \(\frac25mr^2\) each; the two touching the axis also need the parallel axis term.

Answer 1

The Correct Option is C

Step 1: Split into two groups
Group 1: spheres with the axis through the centre. Group 2: spheres whose surface just touches the axis.

Step 2: Add up
Group 1 gives $3\times0.4=1.2$ in units of $mr^2$. Group 2 gives $2\times(0.4+1)=2.8$. Total $4.0\,mr^2$, option (C).

Final Answer:
The total is $4mr^2$, option (C). \[ \boxed{4mr^2} \]