Two masses m1 and m2 are connected by a string passing through a hollow pipe with m1 being swung around in a circle of radius R and m2 hanging vertically as shown in the figure.

Obviously if m1 moves quickly in the circle then m2 will start to move upwards, but if m1 moves slowly m2 will start to fall.
A) Derive an expression for the tension T in the string.
B) Derive an expression for the acceleration of m2 in terms of the period t of the circular motion.
C) For what period t, will the mass m2 be at rest?
D) If the masses are equal, what is the answer to Part C)?
E) For a radius of 9.81 m, what is the numerical value of this period?

m1 R m2