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Standard IX

Mathematics

Length of an Arc

O is a fixed ...

Question

O is a fixed point and P is a point which is at a fixed distance from O. If P moves such that angle between initial and final positions of OP is A $<$ $360^{\circ}$ then the path taken by P is called __.

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Solution

Observe in the above figure that when P moves, the angular position of OP changes and the path taken by P forms an arc. The arc is a portion on the circumference of a circle. Here if the point P had completed one full revolution then the distance covered by it would have been the circumference of the circle. But the point P does not cover one full revolution. Thus the path it covered is an arc.

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O is a fixed point and P is a point which is at a fixed distance from O. If P moves such that angle between initial and final positions of OP is A < 360∘ then the path taken by P is called __.

O is a fixed point and P is a point which is at a fixed distance from O. If P moves such that angle between initial and final positions of OP is A $<$ $360^{\circ}$ then the path taken by P is called __.