Question

A hollow ball with a diameter of 3.72 cm has an average density of 0.0841 g/cm3. What force must be applied to hold it stationary while it is completely submerged under water? (Enter the magnitude in N, and select the direction from the options given.)

Answer 1

Answer:

0.2158 N.

Explanation:

Given , The ball has diameter (d)=3.72 cm = 0.0372 m

radius(r) = d/2 = 1.86 cm = 0.0186 m

Average density= 0.0841 g/cm^3 = 84.1 kg/m^3

There are two forces acting on the ball.. i.e. The buoyancy force and weight of the ball.

The force required to completely submerged under water= Buoyancy force - Weight of ball

buoyancy force = volume×density of water×g

$F_b= \frac{4}{3} \pi r^{3}dg$

$=4.18\times(0.018)^3\times 1000\times9.8$

[ density of water = 1000 kg/m3]

=0.238 N

mass of ball = average density×Volume

=84.1×4.18×(0.018)^3

=0.0022262 kg

Weight of ball = mg = 0.00204×9.81 =0.02219 N

Required force = 0.238 - 0.02219 = 0.2158 N.