3. A flat disk of mass m is moving on a frictionless, horizontal table in a circle with constant radius R. It moves with constant speed. It is held in its path by a massless cord that is connected to a dangling block of R. mass M, through a hole in the center. The block is at rest. V=? a) Derive an expression for the tension in the cord. b) Derive an expression for the speed v of the disk in M terms of M, m. R, and g.II. Gravity and orbits 4. Uranus has a mass of 8.68*10" kg and a radius of 2.33x10 m. Find a symbolic answer and calculate a numerical value for the free-fall acceleration on the surface of Uranus. 5. Jupiter's moon Io has a mass of m= 8.9*10"kg. It is orbiting Jupiter at a distance 4.22x10'm and has an orbital period of 1.77 Earth days. Find a symbolic answer and calculate a numerical value for the mass of Jupiter. 6. The Moon has a radius of 1.74*10'm. It is orbiting the Earth at a distance of 3.84*10'm. taking 27.3 days for a complete revolution. The free-fall acceleration on Moon is 1.62 m/s. From the information given, find the mass of the Moon and the mass of Earth. Derive symbolic answers and calculate numerical values