In an experiment to verify Stokes law, a small spherical ball of radius r and density ρ falls under gravity through a distance h in air before entering a tank of water. If the terminal velocity of the ball inside water is same as its velocity just before entering the water surface, then the value of h is proportional to: (ignore viscosity of air)

Step-by-step solution

The velocity of ball just before striking the surface of water is given by using kinematical equation of motion under the gravity v 2 = u 2 - 2 g y ⇒ v 2 = - 2 g ( - h ) ⇒ v = 2 g h     . . . ( 1 ) Now, the terminal velocity of spherical ball inside the water tank is given by, v T = 2 9 r 2 ( ρ - σ ) g η     . . . ( 2 ) After falling through h the velocity of ball should be equal to its terminal velocity. From equation (1) and (2) we get, ⇒ 2 g h = 2 9 r 2 ( &#96