Question

A youngster is holding a ball with a diameter of 5.60 cm and average density of 0.0837 g/cm³ under water. Determine the force (in N) needed to hold it completely submerged.

magnitude  N

direction ---Select--- upward downward

Answer 1

Gravitational acceleration = g = 9.81 m/s²

Density of water = _w = 1000 kg/m³

Density of ball = = 0.0837 g/cm³ = 83.7 kg/m³

Diameter of the ball = D = 5.6 cm = 0.056 m

Radius of the ball = R = D/2 = 0.028 m

Volume of the ball = V

V = 4R³/3

V = 4(0.028)³/3

V = 9.195 x 10^-5 m³

The density of the ball is lesser then that of water hence the youngster will have to apply force downwards to submerge the ball completely.

Force applied to submerge the ball = F

Vg + F = _wVg

F = (_w - )Vg

F = (1000 - 83.7)(9.195x10^-5)(9.81)

F = 0.826 N

The force needed to completely submerge the ball = 0.826 N downwards