The solid cylinder of length


The solid cylinder of length $80 \mathrm{~cm}$ and mass $M$ has a radius of $20 \mathrm{~cm}$. Calculate the density of the material used if the moment of inertia of the cylinder about an axis CD parallel to $\mathrm{AB}$ as shown

in figure is $2.7 \mathrm{~kg} \mathrm{~m}^{2}$.



  1. $14.9 \mathrm{~kg} / \mathrm{m}^{3}$

  2. $7.5 \times 10^{1} \mathrm{~kg} / \mathrm{m}^{3}$

  3. $7.5 \times 10^{2} \mathrm{~kg} / \mathrm{m}^{3}$

  4. $1.49 \times 10^{2} \mathrm{~kg} / \mathrm{m}^{3}$

Correct Option: , 4


Parallel axis theorem



$2.7=\mathrm{M} \frac{(0.2)^{2}}{2}+\mathrm{M}\left(\frac{0.8}{2}\right)^{2}$


$M=15 k g$

$\Rightarrow \rho=\frac{\mathrm{M}}{\pi \mathrm{r}^{2} \mathrm{~L}}=\frac{15}{\pi(0.2)^{2} \times 0.8}$

$=0.1492 \times 10^{3}$

Ans. 4


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