Question

Figure shows a uniform solid block of mass $M$ and edge lengths $a, b$ and $c$. Its M.I. about an axis through one edge and perpendicular (as shown) to the large face of the block is

• A. $\frac{M}{3}\left(a^{2}+b^{2}\right)$
• B. $\frac{M}{4}\left(a^{2}+b^{2}\right)$
• C. $\frac{7 M}{12}\left(a^{2}+b^{2}\right)$
• D. $\frac{M}{12}\left(a^{2}+b^{2}\right)$

Answer 1

Answer: (A)

$(MI)_{ CG }=M\left(\frac{a^{2}+b^{2}}{12}\right)$
According to the theorem of parallel axis,
$( MI )_{\text {required axis }}=( MI )_{ CG }+M(O A)^{2}$
$=M\left(\frac{a^{2}+b^{2}}{12}\right)+M\left(\frac{a^{2}+b^{2}}{4}\right)$
$=M\left(\frac{a^{2}+b^{2}}{3}\right)$