Question

Two balls of the same radius but densities p1 = 2 p and p2 = 4 pare placed in a

liquid of density p. What is the ratio (the weight of ball 1 in the liquid / the weight of
ball 2 in the liquid)?

Answer 1

W1 = d1 V

W2 = d2 V weight of balls in air (both have same volume0

w2 = (d2 - p) V apparent weight of ball 2 (p * V = buoyant force

w2 / w1 = (d2 - p) / (d1 - p) the liquid exerts the same buoyant force on each ball

Let p be in units of kg / m^3 * g say 1 N / m^3

Suppose d1 = 2 and d2 = 3 N/m^3 and p = .5 N/m^3

The ratio of apparent weights would be

w2 / w1 = (3 - .5) / (2 - .5) = 1.67 to 1