An object is moving on a circular path of a π radius meters at a constant speed of 4.0 m/S. The time required for one revolution is (in sec) 

Concept:

We know, \({\rm{Velocity~(V)}} = \frac{{{\rm{Distance\;Travel~(S)}}}}{{{\rm{Time~(T)}}}}\)

Distance travel on the circular path in one revolution = perimeter of the circular path

S = π × Diameter of the path

S = π × D

where D is the diameter of the circular path

Calculation:

Given:

V = 4 m/sec, Radius = π meter

Hence Diameter (D) = 2π meter

So, S = π × D

S = π × 2 × π

S = 2π²

\(V = \frac{S}{T}\)

\(4 = \frac{2π^2}{T}\)

\(T = \frac{π^2}{2}\ sec\)

Hence time taken by the object in one revolution will be \(\frac{π^2}{2}\) sec