Question

A ball of density ρ₀ falls from rest from a point P onto the surface of a liquid of density ρ in time T. It enters the liquid, stops, moves up, and returns to P in a total time 3T. Neglect the viscosity, surface tension and splashing. The ratio ρ/ρ₀ is equal to 

(a) 1.5 

(b) 2 

(c) 3 

(d) 4 

Answer 1

Correct Answer is: (c) 3

The downward and upward motions must be symmetrical. Hence, the total time spent by the ball inside the liquid is T, i.e., the downward motion of the ball inside the liquid takes time T/2. Hence, its upward acceleration inside the liquid is 2g.

Let its volume be V. Then, inside the liquid,

Vρg - Vρ₀g = Vρ₀(2g) 

or ρ = 3ρ₀.