A spherical steel ball of diameter 40 mm and density $ 8500 kg/m^3$ is dropped in the large mass of water. The coefficient of Drag of the ball in water is given by 0.45.

1. Find terminal velocity of the ball in the water if the ball is dropped in air.

2. Find increase in terminal velocity of the ball.

Take density of the air =$1.25 kg/ m^3$ & Cd = 0.1

Solution :

Given :

1. Diameter of steel ball, $D=40 \mathrm{~mm}=0.04 \mathrm{~m}$

2. Density of ball, $ \rho_{b}=8500 \mathrm{~kg} / \mathrm{m}^{3}$

3. $C_{D}$ for ball in water $=0.45$

Let the terminal velocity in water $=U_{1}$

A) The forces acting on spherical ball are :

(i) Weight

$ W=$ Density of ball $\times g …