A solid of mass 1kg suspended by a string is completely immersed in water. If the in the string is 5N, calculate the upthrust on the solid, the volume of the solid and its density (g=10m/s² density of water=1000kg/m³)
Well, well, well! Looks like our trusty solid is taking a dive into the watery depths. Let's unravel the mysteries, shall we?
First, let's tackle the upthrust. The upthrust on an object submerged in a fluid is equal to the weight of the fluid it displaces. In this case, our solid has a weight of 5N, so the upthrust will also be 5N. Easy-peasy!
Now, let's delve into the voluminous volume of our solid. We know that the upthrust is equal to the weight of the displaced fluid, which is also equal to the weight of the solid. Since the weight of the solid is 5N and the density of water is 1000kg/m³, we can use the formula:
Weight = Mass x Gravity
Rearranging a bit, we find:
Mass = Weight / Gravity
Mass = 5N / 10m/s²
Mass = 0.5 kg
Now, since density is defined as mass divided by volume, we can rearrange the formula once again to find the volume:
Density = Mass / Volume
Rearranging, we get:
Volume = Mass / Density
Volume = 0.5 kg / 1000kg/m³
Volume = 0.0005 m³
And there we have it! The upthrust on the solid is 5N, the volume is 0.0005 m³, and the density is 1000 kg/m³. Now go forth and conquer those submerged calculations with confidence!
To calculate the upthrust on the solid, we need to determine the weight of the water displaced by the solid. The upthrust is equal to the weight of the water displaced.
1. Calculate the weight of the solid:
Weight = mass * gravity
Weight = 1 kg * 10 m/s²
Weight = 10 N
2. Calculate the upthrust on the solid:
Upthrust = Weight of water displaced = Weight of solid
Upthrust = 10 N
3. Calculate the volume of the solid:
Volume of water displaced = mass of water displaced / density of water
Density of water = 1000 kg/m³
Mass of water displaced = mass of solid = 1 kg
Volume of water displaced = 1 kg / 1000 kg/m³ = 0.001 m³
Therefore, the volume of the solid is 0.001 m³.
4. Calculate the density of the solid:
Density = mass / volume
Density = 1 kg / 0.001 m³
Density = 1000 kg/m³
Therefore, the density of the solid is 1000 kg/m³.
In summary:
- Upthrust on the solid = 10 N
- Volume of the solid = 0.001 m³
- Density of the solid = 1000 kg/m³
To calculate the upthrust on the solid, we need to determine the buoyant force acting on it. The buoyant force is equal to the weight of the water displaced by the solid.
1. Calculate the weight of the solid:
The weight of the solid can be calculated using the formula: weight = mass × acceleration due to gravity.
Given that the mass of the solid is 1kg, and the acceleration due to gravity is 10m/s², the weight of the solid is 1kg × 10m/s² = 10N.
2. Calculate the upthrust:
Since the solid is completely immersed in water, the upthrust is equal to the buoyant force acting on it, which is the weight of the water displaced by the solid.
Therefore, the upthrust on the solid is also 10N.
3. Calculate the volume of the solid:
The volume of the solid can be determined using the formula: volume = mass / density.
Given that the mass of the solid is 1kg and the density of water is 1000kg/m³, the volume of the solid is 1kg / 1000kg/m³ = 0.001m³.
4. Calculate the density of the solid:
Density is defined as mass per unit volume. Therefore, the density of the solid is given by the formula: density = mass / volume.
Given that the mass of the solid is 1kg and the volume is 0.001m³, the density of the solid is 1kg / 0.001m³ = 1000kg/m³.
To summarize:
- The upthrust on the solid is 10N.
- The volume of the solid is 0.001m³.
- The density of the solid is 1000kg/m³.
upthrust = (1 kg * g) - 5 N = 10 N - 5 N
the solid displaces 5 N of water ... 500 g ... 500 cm^3
the density is twice the density of water