A wheel which is innitially at rest is subjected to an angular acceleration and it completed 10 rotation in time 't' .Then the time taken by it to complete the next 10 rotation is

Options

A. ` 2 t`
B. `sqrt2 t`
C. `(sqrt2-1)t`
D. `(sqrt2+1)t`

Answer

C

Explanation

`theta_(1)=2pixx10=20 pi`
` theta_(2)=40pi`
`theta_(2)-theta_(1)=40 pi -20 pi =20 pi `
`theta _(1)=(1)/(2) alpha t_(1)^(2)`
`theta_(2)-theta_(1)=(1)/(2) alpha(t_(2)^(2)-t_(1)^(2))`
`(theta_(2)-theta_(1))/(theta_(1))=(t_(2)^(2)-t_(1)^(2))/(t_(1)^(2))`
`(10)/(10)=(t_(2)^(2)-t_(1)^(2))/(t_(1)^(2))`
`t_(1)^(2)=t_(2)^(2)-t_(1)^(2)`
`2t_(1)^(2)=t_(2)^(2)`
`sqrt2t_(1)=t_(2)`
`(t_(2))/(t_(1))=sqrt2`
`(t_(2)-t_(1))/(t_(1))=sqrt2-1`
`t_(2)-t_(1)=(sqrt2-1)t`