Question

A boy is holding a ball with a diameter of 5.30 cm and average density of 0.0841 g/cm³ under water. Determine the force (in N) needed to hold it completely submerged.

magnitude

Answer 1

Here,

let the forces needed is F

radius, r = 0.053/2 m

volume of the ball = 4pi/3 * (0.053/2)^3

volume of the ball = 7.795 *10^-5 m^3

density , p = 0.0841 g/cm^3 = 84.1 Kg/m^3

Now balancing the forces in the vertical direction

- m * g + Buoyant force + F = 0

- 84.1 * 7.795 *10^-5 * 9.8 + 1000 * 7.795 *10^-5 * 9.8 + F = 0

solving for F

F = - 0.699 N

the force needed to be applied is 0.699 N in the downwards direction