A metallic sphere of mass 1 kg and volume 2 x 10^-4 m³ is completely immersed in water. The buoyant force exerted by water on the sphere is :

(Given: density of water = 1000 kg/m³, g= 10 m/s²)

The correct answer is 2 N.

Key Points

• The buoyant force is calculated using Archimedes' principle: Buoyant force = ρ × V × g, where ρ is the density of the fluid, V is the volume of the object submerged, and g is the acceleration due to gravity.
• Given: Density of water (ρ) = 1000 kg/m³, Volume of sphere (V) = 2 × 10⁻⁴ m³, and g = 10 m/s².
• Using the formula: Buoyant force = (1000) × (2 × 10⁻⁴) × (10) = 2 N.
• The buoyant force is independent of the mass of the sphere; it only depends on the displaced fluid's volume and density.
• Therefore, the correct buoyant force exerted by water on the sphere is 2 N.

Additional Information

• Archimedes' Principle:
  • It states that a body immersed in a fluid experiences an upward force equal to the weight of the fluid displaced by it.
  • This principle is fundamental in calculating buoyant forces acting on submerged objects.
• Buoyant Force:
  • The upward force exerted by a fluid on an object submerged in it.
  • It depends on the fluid's density, the object's submerged volume, and gravitational acceleration.
• Density of Water:
  • The standard density of water at room temperature is approximately 1000 kg/m³.
  • It is one of the key parameters used in buoyancy calculations.
• Relation to Gravitational Force:
  • Gravitational acceleration (g) impacts both the object's weight and the buoyant force exerted by the fluid.
  • In standard conditions on Earth, g = 9.8 m/s² (rounded to 10 m/s² for simplicity in calculations).