Why would a person choose to tie a helium-filled balloon to a child's wrist instead of simply having the child hold on to it? a. helium is less dense than air, so it will float above air if the child lets go of the balloon. b. helium is more dense than air, so it will sink below air if the child lets go of the balloon. c. helium is less dense than air, so it will sink below air if the child lets go of the balloon. d. helium is more dense than air, so it will float above air if the child lets go of the balloon.

The ultracentrifuge is an important tool for separating and analyzing proteins. because of the enormous centripetal accelerations, the centrifuge must be carefully balanced, with each sample matched by a sample of identical mass on the opposite side. any difference in the masses of opposing samples creates a net force on the shaft of the rotor, potentially leading to a catastrophic failure of the apparatus. suppose a scientist makes a slight error in sample preparation and one sample has a mass 10 mg larger than the opposing sample. if the samples are 12 cm from the axis of the rotor and the ultracentrifuge spins at 70,000 rpm, what is the magnitude of the net force on the rotor due to the unbalanced samples? ( be thorough on your answer)