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))`
D. `sqrt(a+(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_(2)^(2)+a_(t)^(2))=sqrt(((v^(2))/r)^(2)+a^(2))`