A circular disc made of iron is rotated about its axis at a constant velocity `Omega.` Calculate the percentage change in the linear speed of a particle of the rim as the disc is slowly heated from `20^@C` to `50^@C` keeping the angular velocity constant. Coefficient of linear expansion of iron `=1.2 xx 10^(-5)C^(-1)`.

Explanation

Given, `T_1= 20^@C`, T_2=50^@C`
DeltaT =30^@C, ` alpha =1.2 xx 10^-5/^@C `
`omega remains constant `
` (i) omega=V/R (ii) omega=V'/R'`
`Now, R'=R(1+alpha Delta theta)`
`= R+R xx 1.2 xx 10^-5xx 30 `
` From (i) and(ii)`
` V/R=V'/R'= V'/1.00036R`
` rArr V'=1.00036 V`
` % change =(1.00036V-V)/V xx 100`
` =0.00036 xx 100 `
` =3.6 xx 10^-2 %`