The velocity and acceleration vectors of a particle undergoing circular motion are v =2i^ m/s and a =2i^+4j^m/s2 respectively at an instant of time. The radius of the circle is
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linear velocity of particle in a circle , v = 2i m/s
acceleration of particle in the circle, a = (2i + 4j) m/s²
concept : in circular motion, acceleration of particle should be perpendicular to its velocity.
it is possible when we take vertical component of acceleration i.e., (4j)
[ because we know, unit vector, i is perpendicular upon j. so, 2i will perpendicular upon 4j]
so, |a| = 4, |v| = 2
now, radius of circle, r = |v|²/|a|
= 2²/4 = 4/4 = 1m
hence, radius of circle is 1m
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