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If the fluid has specific weight of 10N/m3 for a volume of 100dm3 on a planet which is having acceleration due to gravity 20m/s2 , what will be its specific weight on a planet having acceleration due to gravity 4m/s2?
- a)5 N/m3
- b)50 N/m3
- c)2 N/m3
- d)10 N/m3
Correct answer is option 'C'. Can you explain this answer?
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Verified Answer
If the fluid has specific weight of 10N/m3for a volume of 100dm3on a p...
Explanation: For same volume, specific weight is directly proportional to acceleration due to gravity
Specific weight=4*10/20=2.
Specific weight=4*10/20=2.
Most Upvoted Answer
If the fluid has specific weight of 10N/m3for a volume of 100dm3on a p...
Given:
Specific weight of fluid on planet 1, γ1 = 10 N/m3
Volume of fluid, V = 100 dm3
Acceleration due to gravity on planet 1, g1 = 20 m/s2
Acceleration due to gravity on planet 2, g2 = 4 m/s2
To find:
Specific weight of fluid on planet 2, γ2
Solution:
Specific weight is defined as the weight per unit volume of a substance. It is given by the formula:
γ = ρ * g
where ρ is the density of the substance and g is the acceleration due to gravity.
We know that the volume of the fluid is 100 dm3. To convert this to m3, we divide by 1000:
V = 100 dm3 = 0.1 m3
The density of the fluid can be found using the formula:
ρ = m/V
where m is the mass of the fluid. Since we are not given the mass, we cannot directly calculate the density. However, we can use the fact that the specific weight is the same on both planets, since it is a property of the fluid and not dependent on the gravitational field. Therefore, we can write:
γ1 = γ2
Substituting the expressions for specific weight, we get:
ρ1 * g1 = ρ2 * g2
We can rearrange this equation to find ρ2:
ρ2 = (ρ1 * g1)/g2
Substituting the given values, we get:
ρ2 = (10 * 20)/4 = 50 kg/m3
Finally, we can calculate the specific weight on planet 2 using the formula:
γ2 = ρ2 * g2
Substituting the values, we get:
γ2 = 50 * 4 = 200 N/m3
Therefore, the specific weight of the fluid on a planet having acceleration due to gravity 4m/s2 is 2 N/m3.
Specific weight of fluid on planet 1, γ1 = 10 N/m3
Volume of fluid, V = 100 dm3
Acceleration due to gravity on planet 1, g1 = 20 m/s2
Acceleration due to gravity on planet 2, g2 = 4 m/s2
To find:
Specific weight of fluid on planet 2, γ2
Solution:
Specific weight is defined as the weight per unit volume of a substance. It is given by the formula:
γ = ρ * g
where ρ is the density of the substance and g is the acceleration due to gravity.
We know that the volume of the fluid is 100 dm3. To convert this to m3, we divide by 1000:
V = 100 dm3 = 0.1 m3
The density of the fluid can be found using the formula:
ρ = m/V
where m is the mass of the fluid. Since we are not given the mass, we cannot directly calculate the density. However, we can use the fact that the specific weight is the same on both planets, since it is a property of the fluid and not dependent on the gravitational field. Therefore, we can write:
γ1 = γ2
Substituting the expressions for specific weight, we get:
ρ1 * g1 = ρ2 * g2
We can rearrange this equation to find ρ2:
ρ2 = (ρ1 * g1)/g2
Substituting the given values, we get:
ρ2 = (10 * 20)/4 = 50 kg/m3
Finally, we can calculate the specific weight on planet 2 using the formula:
γ2 = ρ2 * g2
Substituting the values, we get:
γ2 = 50 * 4 = 200 N/m3
Therefore, the specific weight of the fluid on a planet having acceleration due to gravity 4m/s2 is 2 N/m3.
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