A small metal sphere is dropped from rest into a long column of a viscous liquid at 20^ C . It attains a terminal velocity v₁ , and its initial acceleration at the moment of release is a₁ . The same liquid is then heated to 60^ C , which significantly reduces its viscosity. The experiment is repeated with the same sphere, which now attains a terminal velocity v₂ and has an initial acceleration a₂ . Assuming the densi

Step-by-step solution

The terminal velocity of a sphere falling through a viscous liquid is given by v_t = 2r^2( - )g 9 . When the temperature of the liquid increases from 20^ C to 60^ C , its viscosity decreases. Since v_t is inversely proportional to , the terminal velocity increases, meaning v₂ > v₁ . The initial acceleration of the sphere at the moment it is dropped ( v=0 ) is determined only by gravity and the buoyant force. It is given by a = g (1 - ) , where is the density of the sphere and is the density of the liquid. Since the