A probe is used to monitor the quality of the water in the sea. The probe is suspended by avertical string which is attached to a sphere. The stationary sphere floats in equilibrium on thesurface of the sea, as shown.airseastringsphereprobeThe sphere has a weight of 5.00 N. The probe and string have a combined weight of 2.00 N.The density of the seawater is 1.03 × 10 3 kg m –3 . The upthrust acting on the probe and thread isnegligible.What is the volume of the sphere below the surface of the sea?A 1.98 × 10 –4 m3B 2.97 × 10 –4 m3C 4.95 × 10 –4 m3D 6.93 × 10 –4 m3
Question
A probe is used to monitor the quality of the water in the sea. The probe is suspended by avertical string which is attached to a sphere. The stationary sphere floats in equilibrium on thesurface of the sea, as shown.airseastringsphereprobeThe sphere has a weight of 5.00 N. The probe and string have a combined weight of 2.00 N.The density of the seawater is 1.03 × 10 3 kg m –3 . The upthrust acting on the probe and thread isnegligible.What is the volume of the sphere below the surface of the sea?A 1.98 × 10 –4 m3B 2.97 × 10 –4 m3C 4.95 × 10 –4 m3D 6.93 × 10 –4 m3
Solution
The sphere is in equilibrium, which means the upthrust (buoyant force) on the sphere equals the weight of the sphere.
The upthrust can be calculated using the formula:
Upthrust = Density of fluid * Volume submerged * g
Where:
- Density of fluid is the density of seawater, which is 1.03 × 10^3 kg/m^3
- Volume submerged is what we're trying to find
- g is the acceleration due to gravity, which is approximately 9.81 m/s^2
The weight of the sphere is given as 5.00 N.
Setting the upthrust equal to the weight of the sphere, we get:
Density of fluid * Volume submerged * g = Weight of sphere
Rearranging for Volume submerged, we get:
Volume submerged = Weight of sphere / (Density of fluid * g)
Substituting the given values:
Volume submerged = 5.00 N / (1.03 × 10^3 kg/m^3 * 9.81 m/s^2)
This gives a volume submerged of approximately 4.95 × 10^-4 m^3, which corresponds to option C.
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