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 `underline(L/sqrt2)`.

Explanation:

The length of the diagonal of the square `=sqrt2L`

Half of the diagonal `=(sqrt2L)/2=L/sqrt2`

Moment of inertia of the system about an axis perpendicular to the square and passing through its centre is

`I=4"m"(L/sqrt2)^2=2ML^2`

If k is the radius of gyration

then Mk² = 2ML²

∴ k `=sqrt2  L`