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  • Four spherical shell each of radius a and mass m are palced with their centre on four corner of a square of a side b . What is the MI of given arrangement about any diagonal of the square &nbs

Four spherical shell each of radius a and mass m are palced with their centre on four corner of a square of a side b . What is the MI of given arrangement about any diagonal of the square  

 

Option: 1

\frac{m}{3} [ a^2 + 3b^2]


Option: 2

m [ 4a^2 + b^2]


Option: 3

\frac{m}{3}(8a^{2}+3b^2)


Option: 4

\frac{m}{2} [ a^2 + 4b^2]


Answers (1)

best_answer

As we have learned

Moment of inertia for spherical shell -

I=\frac{2}{3} MR^{2}

 

- wherein

About a diameter.

 

 I = I_1 + I_2 + I_3 + I_4\\ I_ 1 = I_2 \: \: and \: \: I_3 = I_4 \\ I = 2 I_1 +2 I_3

I_1 = \frac{2}{3} ma^2 \\\\I_3 = I_c + md^2 \\\\ = \frac{2}{3}ma^2 + m [\frac{b}{\sqrt 2}]^2\\\\ = 2/3 ma^2 + 1/2 mb^2 \\\\

I = 2I_1 + 2I_3 = \frac{4}{3}ma^2 + \frac{4}{3}ma^2 + mb^2\\\\ = \frac{8}{3}ma^2 + mb^2 = \frac{m}{3} [8a^2 + 3b^2 ]

 

 

 

 

 

Posted by

Gautam harsolia

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