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Two identical balls each having density σ are suspended from a common point by two insulating strings of equal length. Both the balls have equal mass and charge. In equilibrium each string makes an angle theta with vertical. Now if the balls are
suspended in a liquid of
density ρ and the distance between
the balls remains same, then what will be the dielectric constant of the liquid ?
Most Upvoted Answer
Two identical balls each having density σ are suspended from a common ...
Problem: Two identical balls each having density σ are suspended from a common point by two insulating strings of equal length. Both the balls have equal mass and charge. In equilibrium each string makes an angle theta with vertical. Now if the balls are suspended in a liquid of density ρ and the distance between the balls remains same, then what will be the dielectric constant of the liquid?
Solution:
Concepts:
- Electrostatics
- Buoyancy
- Equilibrium of forces
Assumptions:
- The system is in equilibrium in both cases
- The charge on each ball remains the same
- The length of the strings remains the same
- The liquid is incompressible
- The balls are fully submerged in the liquid
Steps:
1. Calculate the tension in the strings in air and in liquid
2. Calculate the buoyant force on each ball in the liquid
3. Equate the net force on each ball in air and in liquid to find the dielectric constant of the liquid
Step 1: Tension in strings
- In air: The tension in each string is equal to the weight of the ball, i.e., T = mg
- In liquid: The tension in each string is equal to the weight of the ball minus the buoyant force, i.e., T = (m - ρV)g, where V is the volume of each ball
Step 2: Buoyant force
- The buoyant force on each ball in the liquid is equal to the weight of the liquid displaced by the ball, i.e., Fb = ρVg, where V is the volume of each ball
Step 3: Equating forces
- In air: The net force on each ball is equal to the tension in the string minus the weight, i.e., mgcosθ = T - mg
- In liquid: The net force on each ball is equal to the tension in the string minus the weight plus the buoyant force, i.e., (m - ρV)gcosθ = T - (m - ρV)g + ρVgcosθ
- Equating the two forces, we get (m - ρV)gcosθ = T - (m - ρV)g + ρVgcosθ
- Simplifying, we get ρVgcosθ = (m - ρV)g
- Solving for ρ, we get ρ = m/(2Vcosθ - 2mσ/ρ)
Answer: The dielectric constant of the liquid is ρ = m/(2Vcosθ - 2mσ/ρ).
Solution:
Concepts:
- Electrostatics
- Buoyancy
- Equilibrium of forces
Assumptions:
- The system is in equilibrium in both cases
- The charge on each ball remains the same
- The length of the strings remains the same
- The liquid is incompressible
- The balls are fully submerged in the liquid
Steps:
1. Calculate the tension in the strings in air and in liquid
2. Calculate the buoyant force on each ball in the liquid
3. Equate the net force on each ball in air and in liquid to find the dielectric constant of the liquid
Step 1: Tension in strings
- In air: The tension in each string is equal to the weight of the ball, i.e., T = mg
- In liquid: The tension in each string is equal to the weight of the ball minus the buoyant force, i.e., T = (m - ρV)g, where V is the volume of each ball
Step 2: Buoyant force
- The buoyant force on each ball in the liquid is equal to the weight of the liquid displaced by the ball, i.e., Fb = ρVg, where V is the volume of each ball
Step 3: Equating forces
- In air: The net force on each ball is equal to the tension in the string minus the weight, i.e., mgcosθ = T - mg
- In liquid: The net force on each ball is equal to the tension in the string minus the weight plus the buoyant force, i.e., (m - ρV)gcosθ = T - (m - ρV)g + ρVgcosθ
- Equating the two forces, we get (m - ρV)gcosθ = T - (m - ρV)g + ρVgcosθ
- Simplifying, we get ρVgcosθ = (m - ρV)g
- Solving for ρ, we get ρ = m/(2Vcosθ - 2mσ/ρ)
Answer: The dielectric constant of the liquid is ρ = m/(2Vcosθ - 2mσ/ρ).
Community Answer
Two identical balls each having density σ are suspended from a common ...
Tan@in air= F/mg
tan@in liquid =F*/mg-v(rho)g m=v (sigma)g
@in air =@in liq F* =F/E ^
E^=sigma-rho/sigma
tan@in liquid =F*/mg-v(rho)g m=v (sigma)g
@in air =@in liq F* =F/E ^
E^=sigma-rho/sigma
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Two identical balls each having density σ are suspended from a common point by two insulating strings of equal length. Both the balls have equal mass and charge. In equilibrium each string makes an angle theta with vertical. Now if the balls are
suspended in a liquid of
density ρ and the distance between
the balls remains same, then what will be the dielectric constant of the liquid ?
Question Description
Two identical balls each having density σ are suspended from a common point by two insulating strings of equal length. Both the balls have equal mass and charge. In equilibrium each string makes an angle theta with vertical. Now if the balls are suspended in a liquid of density ρ and the distance between the balls remains same, then what will be the dielectric constant of the liquid ? for Class 12 2024 is part of Class 12 preparation. The Question and answers have been prepared according to the Class 12 exam syllabus. Information about Two identical balls each having density σ are suspended from a common point by two insulating strings of equal length. Both the balls have equal mass and charge. In equilibrium each string makes an angle theta with vertical. Now if the balls are suspended in a liquid of density ρ and the distance between the balls remains same, then what will be the dielectric constant of the liquid ? covers all topics & solutions for Class 12 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Two identical balls each having density σ are suspended from a common point by two insulating strings of equal length. Both the balls have equal mass and charge. In equilibrium each string makes an angle theta with vertical. Now if the balls are suspended in a liquid of density ρ and the distance between the balls remains same, then what will be the dielectric constant of the liquid ? .
Two identical balls each having density σ are suspended from a common point by two insulating strings of equal length. Both the balls have equal mass and charge. In equilibrium each string makes an angle theta with vertical. Now if the balls are suspended in a liquid of density ρ and the distance between the balls remains same, then what will be the dielectric constant of the liquid ? for Class 12 2024 is part of Class 12 preparation. The Question and answers have been prepared according to the Class 12 exam syllabus. Information about Two identical balls each having density σ are suspended from a common point by two insulating strings of equal length. Both the balls have equal mass and charge. In equilibrium each string makes an angle theta with vertical. Now if the balls are suspended in a liquid of density ρ and the distance between the balls remains same, then what will be the dielectric constant of the liquid ? covers all topics & solutions for Class 12 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Two identical balls each having density σ are suspended from a common point by two insulating strings of equal length. Both the balls have equal mass and charge. In equilibrium each string makes an angle theta with vertical. Now if the balls are suspended in a liquid of density ρ and the distance between the balls remains same, then what will be the dielectric constant of the liquid ? .
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suspended in a liquid of
density ρ and the distance between
the balls remains same, then what will be the dielectric constant of the liquid ? in English & in Hindi are available as part of our courses for Class 12.
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suspended in a liquid of
density ρ and the distance between
the balls remains same, then what will be the dielectric constant of the liquid ? defined & explained in the simplest way possible. Besides giving the explanation of
Two identical balls each having density σ are suspended from a common point by two insulating strings of equal length. Both the balls have equal mass and charge. In equilibrium each string makes an angle theta with vertical. Now if the balls are
suspended in a liquid of
density ρ and the distance between
the balls remains same, then what will be the dielectric constant of the liquid ? , a detailed solution for Two identical balls each having density σ are suspended from a common point by two insulating strings of equal length. Both the balls have equal mass and charge. In equilibrium each string makes an angle theta with vertical. Now if the balls are
suspended in a liquid of
density ρ and the distance between
the balls remains same, then what will be the dielectric constant of the liquid ? has been provided alongside types of Two identical balls each having density σ are suspended from a common point by two insulating strings of equal length. Both the balls have equal mass and charge. In equilibrium each string makes an angle theta with vertical. Now if the balls are
suspended in a liquid of
density ρ and the distance between
the balls remains same, then what will be the dielectric constant of the liquid ? theory, EduRev gives you an
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suspended in a liquid of
density ρ and the distance between
the balls remains same, then what will be the dielectric constant of the liquid ? tests, examples and also practice Class 12 tests.
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