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BITSAT 2012
Exam
BITSAT
Year
2012
Subject
Physics
Chapter
Rotational Motion

BITSAT 2012 · Physics · Rotational Motion

What is the moment of inertia of a solid sphere of density and...

What is the moment of inertia of a solid sphere of density ρ\rho and radius R\mathrm{R} about its diameter?

Options

  1. A105176R5ρ\frac{105}{176} \mathrm{R}^{5} \rho
  2. B105176R2ρ\frac{105}{176} \mathrm{R}^{2} \rho
  3. C176105R5ρ\frac{176}{105} \mathrm{R}^{5} \rho
  4. D176105R2ρ\frac{176}{105} \mathrm{R}^{2} \rho

Correct answer

C. 176105R5ρ\frac{176}{105} \mathrm{R}^{5} \rho

Step-by-step solution

For solid sphere I=25MR2=25(43πR3ρ)R2ρ=176105R5ρ\begin{array}{l} I=\frac{2}{5} M R^{2}=\frac{2}{5}\left(\frac{4}{3} \pi R^{3} \rho\right) R^{2} \\ \rho=\frac{176}{105} R^{5} \rho \end{array}
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