Question

A car is moving along the circle $x^{2}+y^{2}=a^{2}$ in the anti-clockwise direction with a constant speed. The $x-y$ plane is a rough horizontal stationary surface. When the car is at the point $\left(\right.a \, cos\theta , \, a \, sin\theta \left.\right)$ , the unit vector in the direction of the friction force acting on the car is

• A. $\text{cos} \theta \, \hat{\text{i}} + \text{sin} \theta \, \hat{\text{j}}$
• B. $\text{cos}\theta \hat{\text{i}}-\text{sin}\theta \hat{\text{j}}$
• C. $-cos\theta \hat{i}-sin\theta \hat{j}$
• D. $-cos\theta \hat{\text{i}}+\text{sin}\theta \hat{\text{j}}$

Answer 1

Answer: (C)

The direction of the friction force should be towards the centre of the circle which is
$-\hat{r}=-cos\theta \hat{i}-sin\theta \hat{j}$