KCET · Physics · Rotational Motion
Seven identical discs are arranged in a planar pattern, so as to touch each other as shown in the figure. Each disc has mass \(m\) radius \(R\). What is the moment of inertia of system of six discs about an axis passing through the centre of central disc and normal to plane of all discs?
- A \(27 m R^2\)
- B \(100 m R^2\)
- C \(55 \frac{m R^2}{2}\)
- D \(85 \frac{m R^2}{2}\)
Answer & Solution
Correct Answer
(C) \(55 \frac{m R^2}{2}\)
Step-by-step Solution
Detailed explanation
According to question, moment of inertia of
7 discs will be
\(\begin{aligned} I & =I_{\mathrm{COM}}+M d_2 \\ & =\frac{7}{2} M R^2+6 M(2 R)^2\end{aligned}\)
( \(\because\) radius of all 6 discs will be \(2 R\) from centre).
\(=\frac{55}{2} M R^2\)
7 discs will be
\(\begin{aligned} I & =I_{\mathrm{COM}}+M d_2 \\ & =\frac{7}{2} M R^2+6 M(2 R)^2\end{aligned}\)
( \(\because\) radius of all 6 discs will be \(2 R\) from centre).
\(=\frac{55}{2} M R^2\)
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