Take the density of the crown to be . What is the ratio of the crown's apparent weight (in water) to its actual weight ?
I don't have the slightest idea what you are talking about. Probably something about volume. You need to be quite specific about your question and identify any data you have.
To determine the ratio of the crown's apparent weight to its actual weight, we need to consider the concept of buoyancy. The apparent weight of an object submerged in a fluid, such as water, is different from its actual weight due to the buoyant force.
The buoyant force acting on an object in a fluid is equal to the weight of the fluid displaced by the object. This buoyant force counteracts the object's weight and reduces its effective weight, resulting in its apparent weight.
To calculate the ratio of the crown's apparent weight (in water) to its actual weight, we need additional information, such as the density of the crown and the density of water.
Let's denote the actual weight of the crown as W_crown and the apparent weight of the crown in water as W_apparent.
The ratio of the crown's apparent weight to its actual weight can be given by the equation:
W_apparent/W_crown = (W_crown - Buoyant force)/W_crown
The buoyant force can be calculated using the Archimedes' principle, which states that the buoyant force is equal to the weight of the fluid displaced by the object. The weight of the fluid displaced can be found by multiplying the volume of the displaced fluid by the density of water.
Buoyant force = Volume_displaced × Density_water × g
Here, g represents the acceleration due to gravity (~9.8 m/s^2).
To continue with the calculation, we need the density of the crown and the density of water. Please provide those values, and I can help you calculate the ratio of the crown's apparent weight to its actual weight.