Four point masses, each of value m, are placed at the corners of a square A B C D of side l. The moment of inertia of this system about an axis through A and parallel to B D is

Question

Four point masses, each of value m, are placed at the corners of a square A B C D of side l. The moment of inertia of this system about an axis through A and parallel to B D is (A) m l2 (B) 2 m l2 (C) √3 m l2 (D) 3 m l2

Tardigrade Admin · Accepted Answer

A O cos 45°=(l/2) ∴ A O × (1/√2)=(l/2) or A O=(l/√2) I=ID+IB+IC or I=(2 m l2/2)+m((2 l/√2))2 =(2 m l2/2)+(4 m l2/2) or I=(6 m l2/2)=3 m l2

Q. Four point masses, each of value $m$ , are placed at the corners of a square $A BC D$ of side $l$ . The moment of inertia of this system about an axis through $A$ and parallel to $B D$ is

$m l^{2}$

$2 m l^{2}$

$3 m l^{2}$

$3 m l^{2}$

$A O cos 4 5^{\circ} = \frac{l}{2}$
$∴ A O \times \frac{1}{2} = \frac{l}{2}$
or $A O = \frac{l}{2}$
$I = I_{D} + I_{B} + I_{C}$
or $I = \frac{2 m l ^{2}}{2} + m (\frac{2 l}{2})^{2}$
$= \frac{2 m l ^{2}}{2} + \frac{4 m l ^{2}}{2}$
or $I = \frac{6 m l ^{2}}{2} = 3 m l^{2}$

Q. Four point masses, each of value m, are placed at the corners of a square ABCD of side l. The moment of inertia of this system about an axis through A and parallel to BD is

ml2

2ml2

3​ml2

3ml2

AOcos45∘=2l​ ∴AO×2​1​=2l​ or AO=2​l​ I=ID​+IB​+IC​ or I=22ml2​+m(2​2l​)2 =22ml2​+24ml2​ or I=26ml2​=3ml2

Q. Four point masses, each of value $m$ , are placed at the corners of a square $A BC D$ of side $l$ . The moment of inertia of this system about an axis through $A$ and parallel to $B D$ is

$m l^{2}$

$2 m l^{2}$

$3 m l^{2}$

$3 m l^{2}$

$A O cos 4 5^{\circ} = \frac{l}{2}$
$∴ A O \times \frac{1}{2} = \frac{l}{2}$
or $A O = \frac{l}{2}$
$I = I_{D} + I_{B} + I_{C}$
or $I = \frac{2 m l ^{2}}{2} + m (\frac{2 l}{2})^{2}$
$= \frac{2 m l ^{2}}{2} + \frac{4 m l ^{2}}{2}$
or $I = \frac{6 m l ^{2}}{2} = 3 m l^{2}$