The weight of a solid in air is four times greater than the weight of solid in water. Find its weight of which solid in water if it has relative density is 64.
To find the weight of the solid in water, we need to understand the concept of relative density.
Relative density, also known as specific gravity, is the ratio of the density of a substance to the density of a reference substance. In this case, the reference substance is water, which has a relative density of 1.
Given that the relative density of the solid is 64, it means that the solid is 64 times denser than water.
Let's assume the weight of the solid in water is W (in newtons).
According to Archimedes' principle, the weight of an object in air is equal to the weight of that object in water displaced by it. Therefore, the weight of the solid in air is 4 times greater than the weight of the solid in water.
So, the weight of the solid in air would be 4W (in newtons).
Now, considering the relative density of the solid:
Relative density = Density of solid / Density of water
Since the density of water is 1000 kg/m³, we can find the density of the solid as follows:
64 = Density of solid / 1000
Density of solid = 64 * 1000 = 64000 kg/m³
Now, we can use the density formula to find the weight of the solid in water:
Weight of solid in water = Density of solid * Volume of solid * g
Since the volume and g (acceleration due to gravity) are not given in the question, it is not possible to provide the exact weight of the solid in water without that information. However, this is the general formula used to calculate the weight of an object in a particular fluid.
To solve this problem, we need to understand the concept of relative density. Relative density is defined as the ratio of the density of a substance to the density of a reference substance. In this case, the reference substance is water, which has a relative density of 1.
Let's start by assigning some variables:
- Weight of solid in air: W_air
- Weight of solid in water: W_water
- Relative density of the solid: RD = 64
We are given that the weight of the solid in air is four times greater than the weight of the solid in water. Mathematically, this can be expressed as:
W_air = 4 * W_water (Equation 1)
We also know that the relative density (RD) of a substance is the ratio of its density to the density of water. Mathematically:
RD = Density of substance / Density of water
In this case, since the relative density of the solid is given as 64, we can say:
RD = 64 = Density of solid / Density of water
Since the density of water is known to be 1 g/cm^3, we have:
64 = Density of solid / 1
Now, let's rearrange Equation 1 to solve for W_water:
W_water = W_air / 4
Substituting the value of W_water into the equation, we get:
W_air / 4 = 64 * W_water
Since we know that W_air = 4 * W_water, we can substitute that value in:
W_air / 4 = 64 * (W_air / 4)
Simplifying the equation:
1 = 64/4
Now, solving for W_water:
W_water = W_air / 4
W_water = (4 * W_water) / 4
Both sides of the equation are equal, which means the weight of the solid in water is equal to 64 grams.
Therefore, the weight of the solid in water is 64 grams.