An object with mass m is attached to a string with initial length R, and moves on a frictionless table in a circular orbit with center C as shown in the figure. The string is also attached to the center, but its length is adjustable during the motion. The object initially moves with velocity v and angular velocity ω.
Given: m = 500 g, v = π m/s, R = 50 cm
If the length of the string is shortened from R to r = R/2 while the mass is moving, what will be the new period in SI units?
T = (2πR) / v
The Attempt at a Solution
T = (2πR) / v = (2π0.5) / π = 1
=> T = (2πR/2) / v = 0.5 s
But apparently 0.5 is not the correct answer and I do not understand why.