Is this correct??
Metal block weighs 500g in air and 446g completely submerged in water.
Calculate density and relative density.
Density of water = 1000kg/m3
BF (Buoyant force) will be 500g-446g = 0.54 g (or 0.054 kg).
For volume: If BF = Density(water)*V*g
then V = BF/density*g = 0.054/1000*9.81
=5.50*10^-6 m3
Density metal = m/V = 0.50Kg/5.50*10^-6 m3
=90909.10 Kg/m3
Relative density = 90909.10/1000
=90.91
Is this correct???
500 - 446 = 54 g = mass (not weight or force) of water displaced which is 54 cubic centimeters
so
density of block = 500 g/54 cm^3
= 9.26 g/cm^3
= 9260 kg/m^3
9260/1000 = 9.260 = relative density
by the way the relative density of steel is about 8
When the unit is gm you can take it as mass.(To mention weight unit is 'gm-weight'.)
volume of water displaced = volume of block= 54 cc ( mass/density of water displaced = 54gm/1gm per cc)
Thus density of block = mass of block in air / volume of block = 500/54 = 9.26 g/cc
it is correct
Let's go through the calculations step by step to determine if the answer is correct.
1. First, we need to calculate the volume of the metal block.
To do this, we can use Archimedes' principle, which states that the buoyant force acting on an object submerged in a fluid is equal to the weight of the fluid displaced (BF = Density(water) * V * g). Given that the weight of the fluid displaced is equal to the difference in weight between the block in air and the block submerged in water, we have:
BF = Weight in air - Weight submerged in water = 500g - 446g = 54g.
To convert this to kilograms, we divide by 1000:
BF = 54g / 1000 = 0.054 kg.
We also have the density of water, which is given as 1000 kg/m^3.
Now, rearranging the equation BF = Density(water) * V * g, we can solve for V:
V = BF / (Density(water) * g) = 0.054 kg / (1000 kg/m^3 * 9.81 m/s^2) ≈ 5.50 * 10^(-6) m^3.
2. Next, we can calculate the density of the metal block.
The density (ρ) is defined as mass (m) divided by volume (V):
Density = m / V = 500g / (5.50 * 10^(-6) m^3) ≈ 90909.10 kg/m^3.
3. Finally, we can calculate the relative density.
Relative density (RD), 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.
Relative Density = Density of metal / Density of water ≈ 90909.10 kg/m^3 / 1000 kg/m^3 ≈ 90.91.
Based on these calculations, your answer for the density and relative density of the metal block appears to be correct.