A horizontal disc is freely rotating about a vertical axis passing through its centre at the rate of `100` rpm. A bob of wax of mass `20g` falls on the disc and sticks to it a distance of `5cm` from the axis. If the moment of inertia of the disc about the given axis is `2xx10^(-4)kg m^(2)`, find new frequency of rotation of the disc.

Explanation

`I_(1)=` Moment of inertia of the disc `=2xx10^(-4)kgm^(2)`
`I_(2)=` Moment of inertia of the disc `+` Moment of inertia of the bob of wax on the disc
`=2xx10^(-4)+mr^(2)=2xx10^(-4)+20xx10^(-3)(0.05)^(2)`
`=2xx10^(-4)+0.5xx10^(-4)=2.5xx10^(-4)kgm^(2)`
`(n//t)_(1)=100` rpm , `(n//t)_(2)=?`
By the principle of conservation of angular momentum ,
`I_(1)omega_(1)=I_(2)omega_(2)` `I_(1)2pi((n)/(t))_(1)=I_(2)2pi((n)/(t))_(2)`
`2xx10^(-4)xx100=2.5xx10^(-4)((n)/(t))_(2)`
`2xx110^(-4)xx100=2.5xx10^(-4)((n)/(t))_(2)`
`((n)/(t))_(2)=(100xx2)/(2.5)=80` rpm