A metal ball of radius 9 10⁻⁴ ~m and density 10^4 ~kg / m ^3 falls freely under gravity through a distance 'h' and erfters a tank of water. Considering that the metal ball has constant velocity, the value of h is [coefficient of viscosity of water =8.1 10⁻⁴ pa - s , g =10 ~m / s ^2 density of water .=10^3 ~kg / m ^3 ]

Step-by-step solution

Velocity of the ball when the ball hits the surface of water v= 2 g h Terminal velocity of the ball, v= 2 9 r^2 g (P- ) Equating (i) and (ii), 2 g h = 2 9 r^2 g (P- ) Solving for h , h= 2 81 r^4 ( P- )^2 g Substituting the given values in the above equation, we have h = 2 81 (9 10⁻⁴ )^4 ( 10^4-10^3 8.1 10⁻⁴ )^2 ~g =20 ~m