A thin uniform square lamina of side a is placed in the xy plane with its sides parallel to x and y-axes and with its centre coinciding with origin. Its moment of inertia about an axis passing through a point on the y-axis at a distance y - 2a and parallel to x-axis is equal to its moment of inertia about an axis passing through a point on the x-axis at a distance x d and perpendicular to xy-plane. Then, value of d is

Options

A. `(7)/(3)a`
B. `sqrt((47)/(12))a`
C. `(9)/(5)a`
D. `sqrt((51)/(12))a`

Answer

(b)

Explanation

Moment of inertia of square lamina about an axis passing through a point on the y-axis at a distance y - 2a is,
`I_(1)=(ma^(2))/(12)+(4a^(2))`
Moment of inertia of square lamina about an axis passing through a point on the x-axis at a distance of red and perpendicular to xy plane is,
`I_(2)=(ma^(2))/(6)+md^(2)`
`I_(1)=I_(2)` (Given)
` Rightarrow (ma^(2))/(12)+m(4a^(2))=(ma^(2))/(6)+md^(2)`
` Rightarrow (ma^(2))/(12)-(ma^(2))/(6)+4ma^(2)=md^(2)`
`ma^(2)[(1)/(12)+(1)/(6)+4]=md^(2)`
`a^(2)((47)/(12))=d^(2)`
Therefore `a^(2)=asqrt((47)/(12))`