91Ó°ÊÓ

• Density of snow${\mathrm{ÒÏ}}_{snow}=96kg/m^3$.
• Density of skier${\mathrm{ÒÏ}}_{skier}=1020kg/m^3$ .

The buoyant force is the upward force exerted by the liquid on the object that is fully or partially immersed in the fluid. The force is equal to the product of the density of the fluid, gravitational acceleration, and the volume of the immersed object.

By using the relation$\mathbf{}\mathit{F}\mathbf{=}\mathit{ÒÏ}\mathit{g}\mathit{V}$,we can find the percentage of gravitational force offset by the buoyant force.

Formula:

$$\begin{gathered} F_g=mg \\ F=\mathrm{ÒÏ}gV \end{gathered}$$

Here,

$F_g$is the weight.

m is the mass of the object.

g is the gravitational acceleration.

F is buoyant force.

p is the density of the fluid.

Gravitational force is given by

$\begin{array}{rcl}{F}_g& =& mg\\ & =& {\mathrm{ÒÏ}}_{skier}gV\\ & & \end{array}$

Buoyant force is,

$$\begin{gathered} F_b={\mathrm{ÒÏ}}_{snow}gV \\ \frac{F_b}{F_g}=\frac{{\mathrm{ÒÏ}}_{snow}gV}{{\mathrm{ÒÏ}}_{skier}gV} \\ \frac{F_b}{F_g}=\frac{{\mathrm{ÒÏ}}_{snow}}{{\mathrm{ÒÏ}}_{skier}} \end{gathered}$$

Substitute the given values in the above equation.

$\begin{array}{rcl}\frac{F_b}{F_g}& =& \frac{96{\text{kg/m}}^3}{1020{\text{kg/m}}^3}\\ & =& 0.094\\ & =& 9.4\%\\ & & \end{array}$

Percentage of the gravitational force offset by the buoyant force$9.4\%$