Solveeit Logo
Login

Question

Question: Three particles, each of mass m gram, are situated at the vertices of an equilateral triangle ABC of...

Three particles, each of mass m gram, are situated at the vertices of an equilateral triangle ABC of side 1 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-cm2 units will be:

A

3/4 ml2

B

2 ml2

C

5/4 ml2

D

3/2 ml2.

Answer

5/4 ml2

Explanation

Solution

Moment of inertia of the system about axis AX

= IA + IA + IC

= mA(rA)2 + mB(rB)2 + mC(rC)2

= m(0)2 + m(l)2 + m(l cos 60)2

=ml2+ml24=5ml24= m l ^ { 2 } + \frac { m l ^ { 2 } } { 4 } = \frac { 5 m l ^ { 2 } } { 4 }