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Q.

A particle is moving along the circle x²+y²=a²in anticlockwise direction. The x-y plane is a rough horizontal stationary surface. At the point $(acos θ, asin θ)$ , the unit vector in the direction of friction on the particle is

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a

$- (\cos θ \hat{i} + \sin θ \hat{j})$

b

$\sin θ \hat{i} - \cos θ \hat{j}$

c

$\cos θ \hat{i} + \sin θ \hat{j}$

d

$\cos θ \hat{i} - \sin θ \hat{j}$

answer is C.

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Detailed Solution

Friction always opposes the relative motion. So friction is oppose to velocity i.e., along opp. to tangen $Position vector \overset{⇀}{r} = \hat{i} acosθ + \hat{j} asinθ velocity \vec{v} = - \hat{i} asinθ + \hat{j} acosθ unit vector opposite to velocity = \hat{i} sinθ - \hat{j} cosθ$

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