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Three mass points m(1), m(2), m(3)are lo...

Three mass points `m_(1), m_(2), m_(3)`are located at the vertices of an equilateral triangle of length a. What is the moment of 'inertia' of the system about an axis along an axis along the altitude of the triangle passing through `m_(1)`?

A

`(m_(1)+m_(2)+m_(3))a^(2)`

B

`(1)/(4)(m_(2)+m_(3))a^(2)`

C

`(1)/(2)(m_(2)+m_(3))a^(2)`

D

`(m_(2)+m_(3))a^(2)`

Text Solution

Verified by Experts

The correct Answer is:
B

M.I. of the system about the altitude AD is
`I=m_(1)" "["Distance of "m_(1)" from AD"]^(2)+m_(2)[BD]^(2)+m_(3)[BD]^(2)`
`=m_(1)xx0+m_(2)((a)/(2))^(2)+m_(3)((a)/(3))^(2)`
`=(1)/(4)(m_(2)+m_(3))a^(2)`
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