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Question

A particle moves in a circular path (radius=r) in the xy plane.
Suppose that at time t its positions are x(t) and y(t) respectively and θ is the angular position relative to the x axis measured in the counterclockwise sense, then x, y can be related to θ as

A
x=rsinθ and y=rcosθ
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B
x=rcosθ and y=rsinθ
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C
x=r2cosθ and y=r2sinθ
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D
x=r2sinθ and y=r2cosθ
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Solution

The correct option is B x=rcosθ and y=rsinθ
Let the particle's instantaneous position be x(t) and y(t) and it makes an angle θ with the horizontal. As seen from the triangle, the xr=cosθx=rcosθ. Similarly, we can also write yr=sinθy=rsinθ
Thus the instantaneous position of the particle x and y are now expressed in terms of r and θ. This is known as polar coordinates
Thus, option (b) is correct
918798_1004447_ans_4d3abc0e461546e8af264dec15926091.PNG

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