question_answer

Three particles, each of mass m gram, are situated at the vertices of an equilateral triangle ABC of side f. 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) \[\frac{3}{2}m{{\ell }^{2}}\]   

B) \[\frac{3}{4}m{{\ell }^{2}}\]

C) \[2m{{\ell }^{2}}\]      

D) \[\frac{5}{4}m{{\ell }^{2}}\]

Correct Answer: D

Solution :

[d] \[{{I}_{AX}}=m{{(AB)}^{2}}+m{{(OC)}^{2}}\] \[=m{{\ell }^{2}}+m{{(\ell \cos \,{{60}^{o}})}^{2}}\] \[=m{{\ell }^{2}}+m{{\ell }^{2}}/4=5/4m{{\ell }^{2}}\]