A spherical ball of radius 1 mm and density 10.5 g/cc is dropped in glycerine of coefficient of viscosity 9.8 poise and density 1.5 g/cc. Viscous force on the ball when it attains constant velocity is 3696 10^ -x N. The value of x is (Given, g = 9.8 m / s ^2 and = 22 7 )

Step-by-step solution

When the spherical ball attains constant (terminal) velocity, the net force acting on it is zero. The downward weight of the ball is balanced by the upward buoyant force and the viscous force. Viscous force F_v = W - F_B F_v = 4 3 r^3 g - 4 3 r^3 g F_v = 4 3 r^3 ( - ) g Given values in SI units: r = 1 mm = 10⁻³ m = 10.5 g/cc = 10.5 10^3 kg/m ^3 = 1.5 g/cc = 1.5 10^3 kg/m ^3 g = 9.8 m/s ^2 Substituting the values: F_v = 4 3 22 7 (10⁻³)^3 (10.5 10^3 - 1.5 10^3) 9.8 F_v = 4 3 22 7 10⁻⁹ 9000 9.8 F_v = 4 22 3000 9.8 7 1