SATHEE: Rotational Motion Question 206

Rotational Motion Question 206

Question: The moment of inertia of a hollow thick spherical shell of mass M and its inner radius $R_{1}$ and outer radius $R_{2}$ about its diameter is

Options:

A) $\frac{2 M}{5} \frac{(R_{2}^{5} - R_{1}^{5})}{(R_{2}^{5} - R_{1}^{3})}$

B) $\frac{2 M}{5} \frac{(R_{2}^{5} - R_{1}^{5})}{(R_{2}^{3} - R_{1}^{3})}$

C) $\frac{4 M}{5} \frac{(R_{2}^{5} - R_{1}^{5})}{(R_{2}^{3} - R_{1}^{3})}$

D) $\frac{4 M}{3} \frac{(R_{2}^{5} - R_{1}^{5})}{(R_{2}^{3} - R_{1}^{3})}$

Show Answer

Answer:

Correct Answer: A

Solution:

[a]

$ρ = \frac{M}{\frac{4}{3} π (R_{2}^{3} - R_{1}^{3})}$ $I_{s h e l l} = \frac{2}{5} M_{2} R_{2}^{2} - \frac{2}{5} M_{1} R_{1}^{2}$ $ –(1)

$M_{2} = ρ \times \frac{4}{3} π R_{2}^{3}$ $= \frac{M R_{2}^{3}}{(R_{2}^{3} - R_{1}^{3})}; M_{1} = \frac{M R_{1}^{3}}{R_{2}^{3} - R_{1}^{3}}$

Putting values of $M_{1}$ and $M_{2}$ in eq.(1),

$I_{s h e l l} = \frac{2 M}{5} \frac{(R_{2}^{5} - R_{1}^{5})}{(R_{2}^{3} - R_{1}^{3})}$

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Rotational Motion Question 206

Question: The moment of inertia of a hollow thick spherical shell of mass M and its inner radius R1 and outer radius R2 about its diameter is

Options:

Answer:

Solution:

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Question: The moment of inertia of a hollow thick spherical shell of mass M and its inner radius $R_{1}$ and outer radius $R_{2}$ about its diameter is