Three particles, each of mass `m` grams situated at the vertices of an equilateral triangle `AbC` of side `I` cm (as shown in the figure). The moment of inertia of the system about a line `AX` perpendicular to `AB` and in the plane of `ABC`, in gram-cm^2 units will be.
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Options

A. `(3//4) ml^2`
B. `2 m l^2`
C. `(5//4) m l^2`
D. `(3//2)m l^2`

Answer

C

Explanation

( c) Moment of inertia of the system about `AX` is given by
`MI = m_A^(gamma^2)A + m_B r^2B +m_C r^2C`
`MI = m(0)^2 + m(l)^2 + m(l sin 30^@)^2`
=`ml^2 + (ml^2)/(4) = (5)/(4) ml^2`.
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