System Of Particles And Rotational Motion Ques 5
5. Three particles, each of mass $\mathrm{m}$ gram, are situated at the vertices of an equilateral triangle $A B C$ of side $l \mathrm{cm}$ (as shown in the figure). The moment of inertia of the system about a line $A X$ perpendicular to $\mathrm{A} B$ and in the plane of $A B C$, in gram- $\mathrm{cm}^2$ units will be
$[2004]$
(a) $\frac{3}{2} $ $m \ell^2$
(b) $\frac{3}{4} $ $m \ell^2$
(c) $2 $ $m \ell^2$
(d) $\frac{5}{4}$ $ m \ell^2$
Show Answer
Answer:
Correct Answer: 5.(d)
Solution: (d)
$ \begin{aligned} I_{A X} & =m(A B)^2+m(\mathrm{OC})^2 \\ & =m \ell^2+m\left(\ell \cos 60^{\circ}\right)^2 \\ & =m \ell^2+m \ell^2 / 4=5 / 4 \mathrm{m} \ell^2 \end{aligned} $
BETA
