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

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) (M/3)(a2+b2) (B) (M/4)(a2+b2) (C) (7 M/12)(a2+b2) (D) (M/12)(a2+b2)

Tardigrade Admin · Accepted Answer

(MI) CG =M((a2+b2/12)) According to the theorem of parallel axis, ( MI ) text required axis =( MI ) CG +M(O A)2 =M((a2+b2/12))+M((a2+b2/4)) =M((a2+b2/3))

Q. 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

$\frac{M}{3} (a^{2} + b^{2})$

$\frac{M}{4} (a^{2} + b^{2})$

$\frac{7 M}{12} (a^{2} + b^{2})$

$\frac{M}{12} (a^{2} + b^{2})$

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

Q. 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

3M​(a2+b2)

4M​(a2+b2)

127M​(a2+b2)

12M​(a2+b2)