A car of mass M is moving on a horizontal circular path of radius r. At an instant its speed is v and is increasing at a rate a.

(a) The acceleration of the car is towards the centre of the path.

(b) The magnitude of the frictional force on the car is greater than \[\frac{\text{mv}^2}{\text{r}}\]

(c) The friction coefficient between the ground and the car is not less than a/g.

(d) The friction coefficient between the ground and the car is \[\mu = \tan^{- 1} \frac{\text{v}^2}{\text{rg}.}\]

#### Solution

(b) The magnitude of the frictional force on the car is greater than \[\frac{\text{mv}^2}{\text{r}}\]

(c) The friction coefficient between the ground and the car is not less than a/g. If the magnitude of the frictional force on the car is not greater than \[\frac{\text{mv}^2}{\text{r}}\] , it will not move forward, as its speed (v) is increasing at a rate a.