NEET · Physics · STD 11 - 6. system of particles and rotational motion
A sphere of radius \(R\) is cut from a larger solid sphere of radius \(2 R\) as shown in the figure. The ratio of the moment of inertia of the smaller sphere to that of the rest part of the sphere about the Y-axis is _______.
- A \(\frac{7}{8}\)
- B \(\frac{7}{40}\)
- C \(\frac{7}{57}\)
- D \(\frac{7}{64}\)
Answer & Solution
Correct Answer
(C) \(\frac{7}{57}\)
Step-by-step Solution
Detailed explanation
\(I _1 =\frac{2}{5} M (2 R )^2 \)
\( I _2 =\frac{2}{5} mr ^2+ md ^2 \)
\( = \frac{2}{5}\left(\frac{ M }{8}\right) R ^2+\frac{ M }{8}( R )^2 \)
\( = \frac{7 MR ^2}{40} \)
\( I = I _1- I _2=\frac{8 MR ^2}{5}-\frac{7 MR ^2}{40}=\frac{57}{40} MR ^2 \)
\( \frac{ I _2}{ I _1} =\frac{7}{57}\)
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