A small spherical ball of radius 0 . 1 mm and density 10 4 kg m - 3 falls freely under gravity through a distance h before entering a tank of water. If, after entering the water the velocity of ball does not change and it continue to fall with same constant velocity inside water, then the value of h will be ____ m . (Given g = 10 m s - 2 , viscosity of water = 1 . 0 × 10 - 5 N ‐ s m - 2 ).

Step-by-step solution

Using equation of motion, v 2 = u 2 + 2 a s v 2 = 0 + 2 - g - h ⇒ v 2 = 2 g h Initial velocity of ball is v = 2 g h = 20 h . If after entering the water this velocity does not change, then this value should be equal to the terminal velocity. Then, 2 g h = 2 9 r 2 ρ - σ g η , here, ρ is density of ball, σ is density of water and η is viscosity. ⇒ 20 h = 2 9 0 . 1 × 10 - 3 2 10 4 - 10 3 10 1 × 10 - 5 ⇒ 20 h = 2 9 10 - 8 10 - 1 10 3 × 10 1 × 10 - 5 &#