Consider a uniform wire of mass M and length L. It is bent into a semicircle. Its moment of inertia about a line perpendicular to the plane of the wire passing through the centre is:

Question

Consider a uniform wire of mass M and length L. It is bent into a semicircle. Its moment of inertia about a line perpendicular to the plane of the wire passing through the centre is: (A) (1/4) ( ML 2/π2) (B) (2/5) ( ML 2/π2) (C) ( ML 2/π2) (D) (1/2) ( ML 2/π2)

Tardigrade Admin · Accepted Answer

π r=L ⇒ r=(L/π) I=M r2=(M L2/π2)

Q. Consider a uniform wire of mass $M$ and length L. It is bent into a semicircle. Its moment of inertia about a line perpendicular to the plane of the wire passing through the centre is:

$\frac{1}{4} \frac{M L ^{2}}{π ^{2}}$

$\frac{2}{5} \frac{M L ^{2}}{π ^{2}}$

$\frac{M L ^{2}}{π ^{2}}$

$\frac{1}{2} \frac{M L ^{2}}{π ^{2}}$

$π r = L$
$\Rightarrow r = \frac{L}{π}$
$I = M r^{2} = \frac{M L ^{2}}{π ^{2}}$

Q. Consider a uniform wire of mass M and length L. It is bent into a semicircle. Its moment of inertia about a line perpendicular to the plane of the wire passing through the centre is:

41​π2ML2​

52​π2ML2​

π2ML2​

21​π2ML2​