Rotational Motion Question 197
Question: Four point masses, each of value m, are placed at the comers of a square ABCD of side $\ell $ .The moment of inertia of this system about an axis passing through A and parallel to BD is
Options:
A) $2m{{\ell }^{2}}$
B) $\sqrt{3}m{{\ell }^{2}}$
C) $3m{{\ell }^{2}}$
D) $m{{\ell }^{2}}$
Show Answer
Answer:
Correct Answer: C
Solution:
[c]
${{I} _{nn’}}=M.I$
due to the point mass at B+M.I
due to the point mass at $D+M.I$
due to the point mass at C.$=2\times m{{\left( \frac{\ell }{\sqrt{2}} \right)}^{2}}+m{{(\sqrt{2}\ell )}^{2}}=m{{\ell }^{2}}+2m{{\ell }^{2}}=3m{{\ell }^{2}}$
