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Question

Two line segments AB and CD are taken. Initially, the points A & C and B & D are coincident. The line segment CD is rotated about point D such that CD coincides with AB again, when it covers a distance of x. If the distance covered by C is y, the angle subtended by CD with respect to starting point is θ, then find the relation among x,y and θ. Assume that θ is in degrees.


A

x = (y × θ)/360

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B

x = (y × θ)/180

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C

y = (x × θ)/360

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D

y = (x × θ)/260

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Solution

The correct option is C

y = (x × θ)/360


We can see that if CD traverses the circumference of the circle, when it covers a distance x and the angular displacement will be 360

(One full revolution is 360 ) For an angular displacement of θ¸ the distance covered by CD is y.

Hence, x is proportional to 360 and y to θ degrees. Thus x360 = yθ¸

So, y = (x×θ)360


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