An astronaut in an orbiting space craft attaches a mass m to

An astronaut in an orbiting space craft attaches a mass m to a string and whirls it around in uniform circular motion. The radius of the circle is R, the speed of the mass is v, and the tension in the string is F. If the mass, radius, and speed were all to double the tension required to maintain uniform circular motion would be F 2F 4F 8F

Solution

Tension will be equal to centripetal force.

T = m v^2 / R

so F = m v^2 / R

and now m\' = 2m, v\' = 2v and R\' = 2R

F\" = m\' (v\')^2 / R\'   = (2m) (2v)^2 / (2R)

F\' = 4 m v^2 / R = 4 F

Ans(C)