MHT CET · Physics · Rotational Motion
Five solid spheres each of mass \(m\) and radius \(r\) are rotating about an axis \(A\) as shown in figure. Hence the moment of inertia of the system about the axis of rotation A-A' as shown in figure. Hence the moment of inertia of the system about the axis of rotation A-A' is
- A \(6 m r^2\)
- B \(5 m r^2\)
- C \(3 m r^2\)
- D \(4 m r^2\)
Answer & Solution
Correct Answer
(D) \(4 m r^2\)
Step-by-step Solution
Detailed explanation
Moment of inertia of a sphere about diameter is \(\frac{2}{5} m r^2\)
Moment of inertia of a sphere about it tangent using parallel axis theorem
\(\begin{aligned} & I=I_{\mathrm{am}}+m r^2=\frac{2}{5} m r^2+m r^2=\frac{7}{5} m r^2 \\ & I_{\text {total }}=3\left(\frac{2}{5} m r^2\right)+2\left(\frac{7}{5} m r^2\right)=\frac{20}{5} m r^2=4 m r^2\end{aligned}\)
Moment of inertia of a sphere about it tangent using parallel axis theorem
\(\begin{aligned} & I=I_{\mathrm{am}}+m r^2=\frac{2}{5} m r^2+m r^2=\frac{7}{5} m r^2 \\ & I_{\text {total }}=3\left(\frac{2}{5} m r^2\right)+2\left(\frac{7}{5} m r^2\right)=\frac{20}{5} m r^2=4 m r^2\end{aligned}\)
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