Two thin discs each of mass M and radius r are attached as shown to form a rigid body. The rotational inertia of this body about an axis perpendicular to the plane of disc B and passing through its centre is

Options

A. `2 Mr^2`
B. `3 Mr^2`
C. `4 Mr^2`
D. `5 Mr^2`

Answer

D

Explanation

Moment of inertia of each disc about an axis through the centre and perpendicular to the plane is `I_(A) = I_(B) = (1)/(2) Mr^(2)`
Applying theorem of parallel axes , moment of inertia of disc A about the given axis is `I._(A) = (1)/(2) Mr^(2) + M (2r)^(2) = (9)/(2) Mr^(2)`
`therefore I = I._(A) + I_(B) = (9)/(2) Mr^(2) + (1)/(2) Mr^(2) = 5 Mr^(2)`