Two discs rotating about their respective axis of rotation with angular speed `2 rad s^(-1) and 5 rad s^(-1)` are brought into contact such that their axes of rotation coincide. Now, the angular speed of the system becomes `4 rad s^(-1)`. If the moment of inertia of the second disc is `1 xx10^(-3)kg m^(2)` then the moment of inertia of the first disc (in `kg m^(2)`) is

Options

A. `0.25 xx 10 ^(-3)`
B. `1.5 xx 10 ^(-3)`
C. `1.25 xx 10 ^(-3)`
D. `0.75 xx 10 ^(-3)`

Explanation

Relation between angular momentum and moment of inertia
`J = I omega`
where `I _(1) = ?`
`I _(2) = 1 xx 10 ^(-3) kg - m ^(2)`
`omega _(1) = 2 ` rad/s
`omega _(2) = 5` rad/s
`omega = 4` rad/s
So, `J = J_(1) + J _(2)`
`(I _(1) + 1 xx 10 ^(-3)) xx 4 = I _(1) xx 2 + 5 xx 1 xx 10 ^(-3)`
`4 I _(1) + 4 xx 10 ^(-3) = 2 I _(1) + 5 xx 10 ^(-3)`
`2 I _(1) = 1 xx 10^(-3)`
`I _(1) = (1)/(2) xx 10 ^(-3)`
`= 0.5 xx 10 ^(-3) kg - m ^(2)`