JEE Mains · Physics · STD 11 - System of particles and rotational motion
- JEE Mains 2021
- Hard
- MCQ
The solid cylinder of length \(80\, {cm}\) and mass \({M}\) has a radius of \(20\, {cm}\). Calculate the density of the material used if the moment of inertia of the cylinder about an axis \(CD\) parallel to \({AB}\) as shown in figure is \(2.7\, {kg} {m}^{2}\)
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Answer & Solution
Correct Answer
(D) \(149\)
Step-by-step Solution
Detailed explanation
Parallel axis theorem
\({I}={I}_{{CM}}+{Md}^{2}\)
\({I}=\frac{{Mr}^{2}}{2}+{M}\left(\frac{{L}}{2}\right)^{2}\)
\(2.7={M} \frac{(0.2)^{2}}{2}+{M}\left(\frac{0.8}{2}\right)^{2}\)
\(2.7={M}\left[\frac{2}{100}+\frac{16}{100}\right]\)
\({M}=15\, {kg}\)
\(\Rightarrow \rho=\frac{{M}}{\pi {r}^{2} {L}}=\frac{15}{\pi(0.2)^{2} \times 0.8}\)
\(=0.1492 \times 10^{3}\)
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