The velocity of a small ball of mass 0 . 3 g and density 8 g cc - 1 when dropped in a container filled with glycerine becomes constant after some time. If the density of glycerine is 1 . 3 g cc - 1 , then the value of viscous force acting on the ball will be x × 10 - 4 N , the value of x is _____ . [use g = 10 m s - 2 ]

Step-by-step solution

Let F V be the viscous force and F B be the buoyant force acting on the ball. ​​​​​​​ Then, when body moves with constant velocity, F V + F B = M g Or, F V = M g - F B F V = ρ B Vg - ρ L Vg = ρ B - ρ L V g , where, V is the volume of small ball. = 8 - 1 . 3 × 10 3 × 0 . 3 × 10 - 3 8 × 10 3 × 10 = 6 . 7 × 0 . 3 8 × 10 - 2 = 67 × 3 8 × 10 - 4 = 25 . 125 × 10 - 4 = 25 × 10 - 4 N Thus, the value of x = 25 .