A cylinder of length 5cm and uniform cross section area 50.24cm^2 is suspended from a spring balance and totally immersed in water.If the density of the material of the cylinder is 1.25g/m^3.
Determine the upthrust on the cylinder. Take g=10m/s^2
density of water=1000kg/m^3
The buoyant force is equal to the mass of the water displaced which is Fb= rho V g. Be sure to convert cm^3 to m^3 if you're using rho = 1000
Surprised they didn't ask what the scale reads since they gave you the density of the rod.
To determine the upthrust on the cylinder, we need to calculate the weight of the water displaced by the cylinder. Here are the steps to do so:
1. Calculate the volume of the cylinder: Since the cross-sectional area of the cylinder is given as 50.24 cm² and its length is 5 cm, you can multiply these values to get the volume in cubic centimeters (cm³).
Volume = 50.24 cm² x 5 cm = 251.2 cm³.
2. Convert the volume to cubic meters (m³): To make the units consistent, we need to convert the volume from cm³ to m³. Since 1 cm³ = 1 x 10^(-6) m³, we divide the volume by 1 x 10^6.
Volume = 251.2 cm³ ÷ 1 x 10^6 = 0.0002512 m³.
3. Calculate the mass of the water displaced: To find the mass of the water displaced, we multiply the volume (in m³) by the density of water (1000 kg/m³).
Mass of water displaced = Volume x Density of water = 0.0002512 m³ x 1000 kg/m³ = 0.2512 kg.
4. Calculate the weight of the water displaced: Since weight is defined as the mass of an object multiplied by the acceleration due to gravity (g), we multiply the mass of the water displaced by the value of g.
Weight of water displaced = Mass x g = 0.2512 kg x 10 m/s² = 2.512 N.
Therefore, the upthrust on the cylinder is 2.512 N.