An astronaut in an orbiting spacecraft 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
a) f/2
b) f
c) 2f
d) 4f
e) 8f

Along wire of diameter 1 mm is submerged in an oil bath of temperature ∞ 31°c. the wire has an electrical resistance per unit length of 0.01 ω/m. if a current of 103 a flows through the wire and the convection coefficient is 500 w/m2·k, what is the steady-state temperature of the wire? from the time the current is applied, how long does it take for the wire to reach a temperature that is within 1°c of the steady-state value? the properties of the wire are 8000 kg/m3, 500 j/kg·k, and 20 w/m·k.