When a mass is suspended from the end of a spring, it lengthens. For the same mass, the lengthening varies according to the spring used. The spring A opposite measures 8 cm. It lengthens. 1 cm for each 100g mass that is suspended at its end. The spring B measures 5 cm and extends by 1 cm for each 75g mass that is suspended at its end. It is possible to suspend the same mass to these two springs so that they are of the same length, once extended. What is this mass?

Uranium has two naturally occurring isotopes. 238u has a natural abundance of 99.3% and 235u has an abundance of 0.7%. it is the rarer 235u that is needed for nuclear reactors. the isotopes are separated by forming uranium hexafluoride uf6, which is a gas, then allowing it to diffuse through a series of porous membranes. 235uf6 has a slightly larger rms speed than 238uf6 and diffuses slightly faster. many repetitions of this procedure gradually separate the two isotopes. what is the ratio of the rms speed of 235uf6 to that of 238uf6? express your answer to five significant figures.