Question

A solid ball of density half of that of water falls freely under gravity from a height of 19.6m and then enters the water. Upto what depth will the ball go? How much time will it take to come again to the water surface? Neglect air resistance & velocity effects in water. 

Answer 1

 Net force on the ball in water

Let us assume that ball will go up to depth h in water. By work energy theorem 

-mg (19.6) + mg h = 0 

h = 19.6 m 

Upward force F = mg in water Acceleration = g time required to come on surface 

Time required to go inside surface is also 2 sec So total time required = 4 sec