Buoyant force of 26 newton acts on a piece of metal that is completely immersed in ethyl alcohol. what is the volume of metal piece..? (density of ethanol=785.06kg/m³)?

Question

Answer

To determine the volume of the metal piece given the buoyant force acting on it, we can use Archimedes’ Principle. This principle states that the buoyant force acting on a submerged object is equal to the weight of the fluid displaced by the object.

Given Data:
- Buoyant Force (F_b) = 26 N
- Density of Ethyl Alcohol (ρ) = 785.06 kg/m³

Formula for Buoyant Force:
The formula for buoyant force is given by:

F_b = ρ × g × V
Where:
- F_b = Buoyant force
- ρ = Density of the fluid (ethyl alcohol)
- g = Acceleration due to gravity (approximately 9.81 m/s²)
- V = Volume of the object submerged in the fluid

Calculating Volume:
To find the volume (V), we rearrange the formula:

V = F_b / (ρ × g)
Now, substituting the known values:

V = 26 N / (785.06 kg/m³ × 9.81 m/s²)
Calculating the denominator:

ρ × g = 785.06 kg/m³ × 9.81 m/s² = 7716.86 N/m³
Now, substitute back into the volume equation:

V = 26 N / 7716.86 N/m³
Calculating the volume:

V ≈ 0.00337 m³

Final Result:
The volume of the metal piece is approximately:

V ≈ 0.00337 m³
This calculation shows how the buoyant force directly relates to the volume of the object submerged in a fluid, allowing us to derive the volume from the force experienced.

Top Courses for UPSCView all

Current Affairs & Hindu Analysis: Daily, Weekly & Monthly

History for UPSC CSE

Lucent for GK

Indian Polity for UPSC CSE

CSAT Preparation

Top Courses for UPSC

Top Courses for UPSC

Suggested Free Tests

Related Content

About UPSC

UPSC Preparation Material

NCERT Based Study Material

How to Prepare for UPSC Exam?

Famous Books for UPSC Exam

UPSC Subjects

UPSC Optionals

Other Popular Exams

Company