The solid cylinder of length 80cm and mass M has a radius of 20cm. Calculate the density of the material used if the moment of inertial of the cylinder about an axis CD parallel to AB as shown in figure is 2.7 kg m²

Option 1 -

7.5 * 10¹ kg/m³

Option 2 -

1.49 * 10² kg/m³

Option 3 -

14.9 kg/m³

Option 4 -

7.5 * 10² kg/m³

3 Views | Posted 2 months ago

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1 Answer

Answered by

alok kumar singh | Contributor-Level 10

2 months ago

Correct Option - 2

Detailed Solution:

$l_{C D} = \frac{1}{2} M r^{2} + M {(\frac{L}{2})}^{2}$

$\Rightarrow 2.7 = M (\frac{0 . 2^{2}}{2} + \frac{0 . 8^{2}}{4})$

M = 15 kg

Density, $ρ = \frac{M}{π r^{2} L} = \frac{15}{3.14 \times 0 . 2^{2} \times 0.8} = 1.49 \times 1 0^{2} k g / m^{3}$

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The solid cylinder of length 80cm and mass M has a radius of 20cm. Calculate the density of the material used if the moment of inertial of the cylinder about an axis CD parallel to AB as shown in figure is 2.7 kg m²

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The solid cylinder of length 80cm and mass M has a radius of 20cm. Calculate the density of the material used if the moment of inertial of the cylinder about an axis CD parallel to AB as shown in figure is 2.7 kg m2

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The solid cylinder of length 80cm and mass M has a radius of 20cm. Calculate the density of the material used if the moment of inertial of the cylinder about an axis CD parallel to AB as shown in figure is 2.7 kg m²