Aclown balances a small spherical grape at the top of his bald head, which also has the shape of a sphere. after drawing sufficient applause, the grape starts from rest and rolls down without slipping. it will leave contact with the clown's scalp when the radial line joining it to the center of curvature makes what angle with the vertical?

Ahair dryer is basically a duct in which a few layers of electric resistors are placed. a small fan pulls the air in and forces it through the resistors where it is heated. air enters a 1200 w hair dryer at 100 kpa and 22°c and leaves at 47°c. the cross-sectional area of the hair dryer at the exit is 60 cm2. neglecting the power consumed by the fan and the heat losses through the walls of the hair dryer, determine (a) the volume flow rate of air at the inlet and (b) the velocity of the air at the exit.