A car of mass m moves in a horizontal circular path of radius r meter. At an instant its speed is `Vm//s` and is increasing at a rate of a `m//sec^(2)`. Then the acceleration of the car is:

Options

A. `(v^(2))/r`
B. `a`
C. `sqrt(a^(2)+((v^(2))/r)^(2))`
D. `sqrt(u+(v^(2))/r)`

Answer

C

Explanation

Radial acceleration `a_(r)=(v^(2))/r`
Tangential acceleration `a_(t)=a`
`:.` Resultant acceleration ,
`a'=sqrt(a_(r)^(2)+a_(t)^(2)+2a_(r)a_(t) cos theta)`
But here `theta=90^(@)`
`:.cos theta=cos 90^(@)=0`
and `a'=sqrt(a_(r)^(2)+a_(t)^(2))=sqrt(((v^(2))/r)^(2)+a^(2))`