Question

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

Answer 1

Let d is the density of water and V be its volume. So, mass of object is:

Mass, $m=0.8V$

Initially, the potential energy of ball is mgh. After hitting the water the kinetic energy is mgh. So, initially net force is, $0.8Vg\left(downwards\right)$ and due to displaced water force in upwards direction is $dVg\left(upwards\right)$

Net force is , $F=0.2Vg$

So, work done by this force will be equal to energy of ball just before entering the water,

Let x is the distance to which ball will sink

$0.2\times V\times g\times x=0.8\times V\times g\times h$

$0.2\times x=0.8\times 2$

$x=8m$