A) A team of astrononers have proposed to construct a large parabolic telescope mirror by spinning a cylindrical contaier of mercury ( rho = 13,500 kg/m^3). the dsh would be 10 m in diameter and spin at an angular velocity of 0.5 rad/sec. What is the minimum volume of mercury needed to prevent the base of the container from being exposed during operation? Assume that the container has a float bottom and verticle sidewalls, and the liquid is in solidbody rotation.
B) The telescope mirror design was approved and a container must be sized to support the load of the spinning mercury. What is the tension force in the container side-walls assuming that it supports all the pressure acting on the side-walls?