# Let  be the moment of inertia of a uniform plate about an axis  that passes through its centre and is parallel to two of its sides.  is a line in the plane of the plate that passes through the centre of the plate and makes an angle  with . The moment of inertia of the plate about the axis  is then equal to a) b) c) d)

## Question ID - 100737 :- Let  be the moment of inertia of a uniform plate about an axis  that passes through its centre and is parallel to two of its sides.  is a line in the plane of the plate that passes through the centre of the plate and makes an angle  with . The moment of inertia of the plate about the axis  is then equal to a) b) c) d)

3537

(a)

and

From symmetry, and

From theorem of perpendicular axis,

Alternative method:

The relation between  and  should be true for all values of

At

Similarly, at

(By symmetry)

Keeping these things in mind. Only option (a) is correct

Next Question :
 In which of the following cases, the centre of mass of a rod is certainly not at its centre? a) The density continuously increases from left to right b) The density continuously decreases from left to right c) The density decreases from left t right up to the centre and then increases d) The density increases from left to right up to the centre and then decreases