Question

For a uniform rectangular sheet shown in the figure, the ratio of moments of inertia about the axes perpendicular to the sheet and passing through O (the centre of mass) and O' (corner point) is:

विकल्प

• 2/3

• 1/4

• 1/8

• 1/2

Answer 1

1/4

Explanation:

Moment of inertia of a rectangular sheet about an axis passing through O,

I_O = `M/12 (a^2 + b^2)`

= `M/12 [(80)^2 + (60)^2]`

From the parallel axis theorem, moment of inertia about O',

`I_(O^')` = I_O + M(50)²

`I_O /I_(O^') = (M/12 (80^2 + 60^2))/(M/12 (80^2 + 60^2) + M (50)^2)`

= `1/4`