A car is travelling with linear velocity v on a circular road of radius r. If it is increasing its speed at the rate of `a` metre/`sec^2`, then the resultant acceleration will be

Options

A. `sqrt({(v^2)/(r^2)-a^2})`
B. `sqrt({(v^4)/(r^2)+a^2})`
C. `sqrt({(v^4)/(r^2)-a^2})`
D. `sqrt({(v^2)/(r^2)+a^2})`

Answer

B

Explanation

`a_(resultant)=sqrt(a_(radial)^2+a_(ta ng ential))=sqrt((v^2)/(r^2)+a^2)`