JEE Mains · Physics · STD 11 - System of particles and rotational motion
- JEE Mains 2022
- Medium
- MCQ
Match List\(-I\) with List\(-II\)
| List \(-I\) | List \(-II\) |
| \((A)\) Moment of inertia of solid sphere of radius \((R)\) about any tangent | \((I)\) \(\frac{5}{3} MR ^{2}\) |
| \((B)\) Moment of inertia of hollow sphere of radius \((R)\) about any tangent | \((II)\) \(\frac{7}{5} MR ^{2}\) |
| \((C)\) Moment of inertia of circular ring of radius \((R)\) about its diameter. | \((III)\) \(\frac{1}{4} MR ^{2}\) |
| \((D)\) Moment of inertia of circular disc of radius \((R)\) about any diameter. | \((IV)\) \(\frac{1}{2} MR ^{2}\) |
Pick an option to check your answer.
Answer & Solution
Correct Answer
(A) \(A-II, B-II, C-IV, D-III\)
Step-by-step Solution
Detailed explanation
\(I _{0}= I _{ com }+ MR ^{2}\)
(Parallel Axis theorem)
\(I_{0}=\frac{2}{5} M^{2}+M^{2}\)
\(I_{0}=\frac{7}{5} M R^{2}\)
Hollow sphere
\(I_{0}=I_{\text {com }}+M^{2}\)
\(=\frac{2}{3} M^{2}+M^{2}=\frac{5}{3} M^{2}\)
\(I _{1}+ I _{2}+ I _{3}\) (Perpendicular axis theorem)
By symmetry MOI
About \(1"\) and \(2"\) Axis are same i.e.
\(I _{1}= I _{2}\)
\(\therefore 2 I_{1}=I_{3}=M^{2}\left(I_{\text {com }}=M^{2}\right)\)
\(I_{1}=\frac{M R^{2}}{2}\)
Similarly in disc
\(2 I_{1}=\frac{M R^{2}}{2}\left\{I_{\text {com }}=\frac{M^{2}}{2}\right\}\)
\(I _{1}=\frac{ MR ^{2}}{4}\)
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