A spherical cavity is excised from the inside of the sphere. The cavity has radius a4 and is centered at position h⃗ , where |h⃗ |<34a, so that the entire cavity is contained within the larger sphere. Find the electric field inside the cavity. Express your answer as a vector in terms of any or all of rho (Greek letter rho), ϵ0, r⃗ , and h⃗ .

Amerry-go-round of radius r, shown in the figure, is rotating at constant angular speed. the friction in its bearings is so small that it can be ignored. a sandbag of mass m is dropped onto the merry-go-round, at a position designated by r. the sandbag does not slip or roll upon contact with the merry-go-round. how would you rank the following different combinations of m and r on the basis of the angular speed of the merry-go-round after the sandbag "sticks" to the merry-go-round from largest to smallest. a) m = 10kg, r = 0.25r b) m = 20kg, r = 0.25r c) m = 10kg, r = 0.50r d) m = 10kg, r = 1.0r e) m = 15kg, r = 0.75r f) m = 40kg, r = 0.25r