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  • 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 m2 . <img alt="" src="h

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 m2 .

Option: 1 1\cdot 49\times 10^{2} \frac{kg}{m^{3}}
Option: 2 7\cdot 5\times 10^{1} \frac{kg}{m^{3}}
Option: 3 14\cdot 9 \frac{kg}{m^{3}}
Option: 4 7\cdot 5\times 10^{2} \frac{kg}{m^{3}}

Answers (1)

best_answer

I_{CD}= I_{AB}+Md^{2}
         = \left ( \frac{MR^{2}}{2} \right )+M\left ( \frac{L}{2} \right )^{2}
2\cdot 7=\left (\frac{M\times0\cdot 04}{2} \right )+\left (\frac{M\times0\cdot 64}{4} \right )
10\cdot 8=0\cdot 08 \, M+0\cdot 64 \, M
10\cdot 8=0\cdot 72 \, M
M= \frac{10\cdot 8}{0\cdot 72}= 15\, kg
M= \rho \times\left ( \pi r^{2} L\right )
s= \frac{15}{\frac{22}{7}\times0\cdot 04\times0\cdot 8}
s= \frac{105}{22\times0\cdot 04\times0\cdot 8}= \frac{105\times 10^{+3}}{22\times 32}
= 0\cdot 149\times 10^{3}
s= 1\cdot 49\times 10^{2}\frac{kg}{m^{3}}  
The correct option is (1)

Posted by

vishal kumar

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