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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)

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Solution

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(downwards) and due to displaced water force in upwards direction is dVg(upwards)

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×V×g×x=0.8×V×g×h

0.2×x=0.8×2

x=8m


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