To calculate the upthrust (buoyant force) experienced by a piece of stone when it is fully submerged in water, we will go through the following steps:
1. Convert the volume of the stone from cm³ to m³:
- The given volume of the stone is [tex]\( 400 \text{ cm}^3 \)[/tex].
- Conversion factor: [tex]\( 1 \text{ cm}^3 = 1 \times 10^{-6} \text{ m}^3 \)[/tex].
- Volume in m³ is [tex]\( 400 \text{ cm}^3 \times 1 \times 10^{-6} \text{ m}^3/\text{cm}^3 \)[/tex].
[tex]\[
\text{Volume of the stone} = 0.0004 \text{ m}^3
\][/tex]
2. Identify the given density of water and the acceleration due to gravity:
- Density of water, [tex]\( \rho_{\text{water}} = 1000 \text{ kg/m}^3 \)[/tex].
- Acceleration due to gravity, [tex]\( g = 9.81 \text{ m/s}^2 \)[/tex].
3. Calculate the upthrust (buoyant force) using the formula:
[tex]\[
\text{Upthrust, } F = \rho \times V \times g
\][/tex]
Where:
- [tex]\( \rho \)[/tex] is the density of the fluid (water in this case).
- [tex]\( V \)[/tex] is the volume of the object submerged in the fluid.
- [tex]\( g \)[/tex] is the acceleration due to gravity.
Substitute the values into the formula:
[tex]\[
F = 1000 \text{ kg/m}^3 \times 0.0004 \text{ m}^3 \times 9.81 \text{ m/s}^2
\][/tex]
4. Perform the multiplication to find the upthrust:
[tex]\[
F = 1000 \times 0.0004 \times 9.81
\][/tex]
5. Calculate the numerical result:
[tex]\[
F \approx 3.92 \text{ N}
\][/tex]
Thus, the upthrust (buoyant force) acting on the stone when it is fully submerged in water is approximately [tex]\( 3.92 \text{ N} \)[/tex].
