A ball of relative density 0.8 falls into water from a height of 2 m. find the depth to which the ball will sink (neglect viscous forces)

Explanation

To solve the problem of finding the depth to which a ball of relative density 0.8 will sink in water after falling from a height of 2 meters, we can follow these steps:

### Step 1: Determine the acceleration of the ball when it enters the water.
- The weight of the ball (downward force) is given by \( W = mg \).
- The buoyant force acting on the ball when it is submerged is \( F_b = V \cdot \rho_w \cdot g \), where \( V \) is the volume of the ball and \( \rho_w \) is the density of water.
- The net force acting on the ball when it is submerged is \( F_{net} = mg - F_b \).
- The mass of the ball can be expressed in terms of its density: \( m = V \cdot \rho_b \), where \( \rho_b \) is the density of the ball.
- The relative density of the ball is given as \( 0.8 \), which means \( \frac{\rho_b}{\rho_w} = 0.8 \) or \( \rho_b = 0.8 \cdot \rho_w \).
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