Moment of inertia of a body about two perpendicular axes X and Y in the plane of lamina are `20" kg m"^2 and 25 "kg m"^2` respectively. Its moment of inertia about an axis perpendicular to the plane of the lamina and passing through the point of intersection of X and Y axes is

Options

A. `5 " kg m"^2`
B. `45 " kg m"^2`
C. `12.5 " kg m"^2`
D. `500 " kg m"^2`

Answer

B

Explanation

Here,
Moment of inertia of the body about X axis,
`I_x = 20 kg m^2 and ` about Y axis , `I_Y = 25 kg m^2` By the theorem of perpendicular axes, the moment of inertia of the body about the given axis (i.e ., Z axis) is
`I_z=I_X+I_Y=(20+25)"kg m"^2= 45 " kg m"^2`