A car is moving along the circle x2+y2=a2 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 (.a cosθ , a sinθ .) , the unit vector in the direction of the friction force acting on the car is

Question

A car is moving along the circle x2+y2=a2 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 (.a cosθ , a sinθ .) , the unit vector in the direction of the friction force acting on the car is (A)  textcos θ hat texti + textsin θ hat textj (B)  textcosθ hat texti- textsinθ hat textj (C) -cosθ hati-sinθ hatj (D) -cosθ hat texti+ textsinθ hat textj

Tardigrade Admin · Accepted Answer

<img class="img-fluid question-image" alt="Solution" src="https://cdn.tardigrade.in/q/nta/p-pvvqie0kaakl.png" /> The direction of the friction force should be towards the centre of the circle which is - hatr=-cosθ hati-sinθ hatj

$cos θ \hat{i} + sin θ \hat{j}$

$cos θ \hat{i} - sin θ \hat{j}$

$- cos θ \hat{i} - s in θ \hat{j}$

$- cos θ \hat{i} + sin θ \hat{j}$

The direction of the friction force should be towards the centre of the circle which is
$- \overset{r}{^} = - cos θ \hat{i} - s in θ \hat{j}$

Q. A car is moving along the circle x2+y2=a2 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 (acosθ,asinθ) , the unit vector in the direction of the friction force acting on the car is

cosθi^+sinθj^​

cosθi^−sinθj^​

−cosθi^−sinθj^​

−cosθi^+sinθj^​

The direction of the friction force should be towards the centre of the circle which is −r^=−cosθi^−sinθj^​

$cos θ \hat{i} + sin θ \hat{j}$

$cos θ \hat{i} - sin θ \hat{j}$

$- cos θ \hat{i} - s in θ \hat{j}$

$- cos θ \hat{i} + sin θ \hat{j}$

The direction of the friction force should be towards the centre of the circle which is
$- \overset{r}{^} = - cos θ \hat{i} - s in θ \hat{j}$