Question

A wooden ball is held under water with a string. The weight of the ball is 400N and its density is 500kg/m^3. Find the tension force of the string on the ball (density of water is 1000 kg/m^3)

Answer 1

We will use the Archimedes' priciple here to calculate the upthrust on the ball due to water, and use that to calculate the net force on the ball. The net force will give us the tension in the string. Let the mass of the ball be m_b, its volume be V, and the mass of the water displaced by it be m_w.

So, the forces acting on the wooden ball are:

1) The weight m_bg acting downwards, given to be 400N.

    Thus,

     Volume of ball, V = mass of ball/density of ball

2) The upthrust due to water acting upwards. According to the Archimedes' principle, this is equal to the weight of water displaced.

Now, weight = m_wg = V*density_water*g

So, the net force on the ball is =

This gives the tension in the string. The negative sign shows that the tension acts in the upward direction. (Notice that the weight of the ball is less than the weight of water displaced by it, so the ball will float on the surface. To keep it submerged under water, you need to pull it downward with the string, hence the tension on the string is in the upward direction)