Question

Four particles each of mass ‘M’ are placed at corners of a square of side ‘L’. The radius of gyration of the system about an axis perpendicular to the square and passing through its centre is ______.

Options

• `L/sqrt2`

• `L/sqrt8`

• `L/sqrt5`

• `L/sqrt3`

Answer 1

Four particles each of mass 'M' are placed at corners of a square of side 'L'. The radius of gyration of the system about an axis perpendicular to the square and passing through its centre is `bbunderline(L/sqrt2)`.

Explanation:

Length of the diagonal of the square

d = `Lsqrt2`

Distance of each corner from the centre 

r = `d/2 = (Lsqrt2)/2 = L/2`

Moment of inertia about the axis through the centre and perpendicular to the plane

There are four masses of mass M:

`I = 4Mr^2 = 4M (L/sqrt2)^2`

`4M xx (L^2)/2 = 2ML^2`

Total mass of the system

M_total = 4M

Radius of gyration (k):

Using I = M_totalk²:

2ML² = 4Mk²

`k^2 = (L^2)/2`

k = `L/sqrt2`