Question

A metal cube is 2.0 cm on each edge. calculate the bouyant force on it when it is completely submerged in oil of density 864 kg/m

Answer 1

Answer:

$6912$ × $10^{-5} Nm/m^{2}$

Explanation:

Density of oil = 864 kg/m = D

Length of each side of the metal cube = 2.0cm = $\frac{2}{100}m$

Area of cross section = $l^{2}$ = $(\frac{2}{100})^{2} = \frac{4}{10000} m^{2}$ = A

Height of cube = h = $\frac{2}{100}m$

Acceleration due to gravity = g = $9.8 m^{2}/sec$ = (For convenience, we would take it as $10 m^{2}/sec$)

Since Upthrust or Bouyant force = A x h x D x g

                                                  U = 4/10000 x 2/100 x 864 x 10

                                                  U = $\frac{6912}{10^{5} }Nm/m^{2}$

Answer 2

Given : Metal cube is 2.0 cm on each edge.

            Density of oil = 864 kg/m.

To Find : Bouyant force on it when it is completely submerged in oil

Solution :

Density of oil = 864 kg/m = D

Length of each side of the metal cube l = 2.0cm = $\[\frac{2}{{100}}m\]$

Area of cross section = $\[{l^2}\]$ = $\[\frac{4}{{10000}}{m^2}\]$

Height of cube = h = $\[\frac{2}{{100}}m\]$

Acceleration due to gravity = 10 m/$\[{s^2}\]$.

Upthrust or Bouyant force = A x h x D x g

Putting value in this equation

Bouyant Force =  $\[\frac{4}{{10000}} \times \frac{2}{{100}} \times 864 \times 10\]$

Bouyant Force = $\[\frac{{6912}}{{{{10}^5}}}\]$ N

Hence ,Bouyant force on cube when it is completely submerged in oil is  $\[\frac{{6912}}{{{{10}^5}}}\]$ N.