Four particles each of mass m are placed at the corners of a square of side length ℓ . The radius of gyration of the system about an axis perpendicular to the square and passing through its centre is

Question

Four particles each of mass m are placed at the corners of a square of side length ℓ . The radius of gyration of the system about an axis perpendicular to the square and passing through its centre is (A) (ℓ/√2) (B) ℓ (C) (ℓ/2) (D) (√2) ℓ

Tardigrade Admin · Accepted Answer

Moment of inertia of system about point P=4 m[(1/√2)]2=2 m ℓ2 and 4 m k2=2 m ℓ2 ∴ k =(ℓ/√2)

Q. Four particles each of mass $m$ are placed at the corners of a square of side length $ℓ .$ The radius of gyration of the system about an axis perpendicular to the square and passing through its centre is

$\frac{ℓ}{2}$

$ℓ$

$\frac{ℓ}{2}$

$(2) ℓ$

Moment of inertia of system about point
$P = 4 m [\frac{1}{2}]^{2} = 2 m ℓ^{2}$ and $4 m k^{2} = 2 m ℓ^{2}$
$∴ k = \frac{ℓ}{2}$

Q. Four particles each of mass m are placed at the corners of a square of side length ℓ. The radius of gyration of the system about an axis perpendicular to the square and passing through its centre is

2​ℓ​

ℓ

2ℓ​

(2​)ℓ

Moment of inertia of system about point P=4m[2​1​]2=2mℓ2 and 4mk2=2mℓ2 ∴k=2​ℓ​

Q. Four particles each of mass $m$ are placed at the corners of a square of side length $ℓ .$ The radius of gyration of the system about an axis perpendicular to the square and passing through its centre is

$\frac{ℓ}{2}$

$ℓ$

$\frac{ℓ}{2}$

$(2) ℓ$

Moment of inertia of system about point
$P = 4 m [\frac{1}{2}]^{2} = 2 m ℓ^{2}$ and $4 m k^{2} = 2 m ℓ^{2}$
$∴ k = \frac{ℓ}{2}$