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QJEEM21Ph8be3: JEE Main 2021 Physics - Class 11 JEEM21Ph8be3 Solution: The solid cylinder of length 80 cm and mass M has a radius of…

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.

JEE Main 2021 (Online) 26th August Evening Shift Physics - Rotational Motion Question 86 English

Multiple Choice Options

  • A 14.9 kg/m3
  • B 7.5 ×\times 101 kg/m3
  • C 7.5 ×\times 102 kg/m3
  • D 1.49 ×\times 102 kg/m3

Step-by-Step Verified Solution

Parallel axis theorem

I = ICM + Md2

I=Mr22+M(L2)2I = {{M{r^2}} \over 2} + M{\left( {{L \over 2}} \right)^2}

2.7=M(0.2)22+M(0.82)22.7 = M{{{{(0.2)}^2}} \over 2} + M{\left( {{{0.8} \over 2}} \right)^2}

2.7=M[2100+16100]2.7 = M\left[ {{2 \over {100}} + {{16} \over {100}}} \right]

M = 15 kg

⇒ρ=Mπr2L=15π(0.2)2×0.8\Rightarrow \rho = {M \over {\pi {r^2}L}} = {{15} \over {\pi {{(0.2)}^2} \times 0.8}}

= 0.1492 ×\times 103

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