Question

A platinum sphere with radius 0.0189 m is totally immersed in mercury. Find the weight of the sphere, the buoyant force acting on the sphere, and the sphere's apparent weight. The densities of platinum and mercury are 2.14 × 10^4 kg/m³ and 1.36 × 10^4 kg/m³, respectively.

Weight: ________
Buoyant Force: ________
Apparent Weight: ________

Answer 1

To find the weight, calculate the platinum sphere's volume and multiply it by the density and gravitational acceleration. The buoyant force is the volume multiplied by the density of mercury and acceleration due to gravity. Apparent weight is the actual weight minus the buoyant force.

Step-by-step explanation:

To find the weight of the platinum sphere, use the formula Weight (W) = mass (m) × acceleration due to gravity (g), where mass is calculated from the sphere's volume and density.

Calculating Weight:

The volume (V) of a sphere is given by V = 4/3 πr³. First, calculate the sphere's volume. Then, multiply the volume by the density of platinum (ρPt) to get the mass. Finally, multiply the mass by gravitational acceleration (9.8 m/s²) to find the weight.

Buoyant Force and Apparent Weight:

Next, calculate the buoyant force (FB) using Archimedes' principle: FB = ρHgVg, where ρHg is the density of mercury, and g is the acceleration due to gravity. The apparent weight of the sphere is the weight minus the buoyant force. Calculate the apparent weight using W - FB.