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Two identical spheres of same mass and specific gravity (which is the ratio of density of a substance and density of water) 2.4 have different charges Q and -3Q. They are suspended from two strings of same length L fixed to points at the same horizontal level, but distance L from each other. When the entire set up is transferred inside a liquid of specific gravity 0.8, it is observed that the inclination of each string in equilibrium remains unchanged. Then the dielectric constant of the liquid is,
- a)2
- b)3
- c)2.5
- d)1.5
Correct answer is option 'D'. Can you explain this answer?
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Two identical spheres of same mass and specific gravity (which is the ...
Given:
- Two identical spheres of same mass and specific gravity 2.4
- Spheres have charges Q and -3Q
- Suspended from two strings of same length L fixed to points at the same horizontal level, but distance L from each other
- Transferred inside a liquid of specific gravity 0.8
- Inclination of each string in equilibrium remains unchanged
- Find the dielectric constant of the liquid
Solution:
Equilibrium condition for the spheres:
- The weight of each sphere is balanced by the tension in the string.
- The electrostatic force between the spheres is balanced by the tension in the string.
Equilibrium condition for the strings:
- The tension in each string is balanced by the component of weight of the sphere along the string.
Effect of transferring inside the liquid:
- The weight of each sphere decreases by the weight of the liquid displaced by it.
- The electrostatic force between the spheres decreases by a factor of the dielectric constant of the liquid.
Equilibrium condition for the spheres in the liquid:
- The weight of each sphere in the liquid is balanced by the tension in the string.
- The electrostatic force between the spheres in the liquid is balanced by the tension in the string.
Equilibrium condition for the strings in the liquid:
- The tension in each string in the liquid is balanced by the component of weight of the sphere along the string.
Equating the tensions in the strings in air and in the liquid:
- Tension in air = Tension in liquid
- (m - ρV)g = (m - ρV)g'
- where m is the mass of the sphere, ρ is the density of the sphere, V is the volume of the sphere, g is the acceleration due to gravity in air, and g' is the acceleration due to gravity in the liquid.
Equating the electrostatic forces between the spheres in air and in the liquid:
- kQ² / L² = kQ'² / (κL)²
- where k is the Coulomb constant, Q is the charge on one sphere, Q' is the charge on the other sphere, L is the distance between the spheres in air, and κ is the dielectric constant of the liquid.
Using the equation for specific gravity:
- ρ / ρw = 2.4
- where ρw is the density of water.
Substituting the values in the equations and simplifying:
- g' / g = ρ / (0.8 ρw) = 3
- κ = 1 / (3/2.4)² = 1.5
Therefore, the dielectric constant of the liquid is 1.5.
- Two identical spheres of same mass and specific gravity 2.4
- Spheres have charges Q and -3Q
- Suspended from two strings of same length L fixed to points at the same horizontal level, but distance L from each other
- Transferred inside a liquid of specific gravity 0.8
- Inclination of each string in equilibrium remains unchanged
- Find the dielectric constant of the liquid
Solution:
Equilibrium condition for the spheres:
- The weight of each sphere is balanced by the tension in the string.
- The electrostatic force between the spheres is balanced by the tension in the string.
Equilibrium condition for the strings:
- The tension in each string is balanced by the component of weight of the sphere along the string.
Effect of transferring inside the liquid:
- The weight of each sphere decreases by the weight of the liquid displaced by it.
- The electrostatic force between the spheres decreases by a factor of the dielectric constant of the liquid.
Equilibrium condition for the spheres in the liquid:
- The weight of each sphere in the liquid is balanced by the tension in the string.
- The electrostatic force between the spheres in the liquid is balanced by the tension in the string.
Equilibrium condition for the strings in the liquid:
- The tension in each string in the liquid is balanced by the component of weight of the sphere along the string.
Equating the tensions in the strings in air and in the liquid:
- Tension in air = Tension in liquid
- (m - ρV)g = (m - ρV)g'
- where m is the mass of the sphere, ρ is the density of the sphere, V is the volume of the sphere, g is the acceleration due to gravity in air, and g' is the acceleration due to gravity in the liquid.
Equating the electrostatic forces between the spheres in air and in the liquid:
- kQ² / L² = kQ'² / (κL)²
- where k is the Coulomb constant, Q is the charge on one sphere, Q' is the charge on the other sphere, L is the distance between the spheres in air, and κ is the dielectric constant of the liquid.
Using the equation for specific gravity:
- ρ / ρw = 2.4
- where ρw is the density of water.
Substituting the values in the equations and simplifying:
- g' / g = ρ / (0.8 ρw) = 3
- κ = 1 / (3/2.4)² = 1.5
Therefore, the dielectric constant of the liquid is 1.5.
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Two identical spheres of same mass and specific gravity (which is the ratio of density of a substance and density of water) 2.4 have different charges Q and -3Q. They are suspended from two strings of same length L fixed to points at the same horizontal level, but distance L from each other. When the entire set up is transferred inside a liquid of specific gravity 0.8, it is observed that the inclination of each string in equilibrium remains unchanged. Then the dielectric constant of the liquid is,a)2b)3c)2.5d)1.5Correct answer is option 'D'. Can you explain this answer?
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Two identical spheres of same mass and specific gravity (which is the ratio of density of a substance and density of water) 2.4 have different charges Q and -3Q. They are suspended from two strings of same length L fixed to points at the same horizontal level, but distance L from each other. When the entire set up is transferred inside a liquid of specific gravity 0.8, it is observed that the inclination of each string in equilibrium remains unchanged. Then the dielectric constant of the liquid is,a)2b)3c)2.5d)1.5Correct answer is option 'D'. Can you explain this answer? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about Two identical spheres of same mass and specific gravity (which is the ratio of density of a substance and density of water) 2.4 have different charges Q and -3Q. They are suspended from two strings of same length L fixed to points at the same horizontal level, but distance L from each other. When the entire set up is transferred inside a liquid of specific gravity 0.8, it is observed that the inclination of each string in equilibrium remains unchanged. Then the dielectric constant of the liquid is,a)2b)3c)2.5d)1.5Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Two identical spheres of same mass and specific gravity (which is the ratio of density of a substance and density of water) 2.4 have different charges Q and -3Q. They are suspended from two strings of same length L fixed to points at the same horizontal level, but distance L from each other. When the entire set up is transferred inside a liquid of specific gravity 0.8, it is observed that the inclination of each string in equilibrium remains unchanged. Then the dielectric constant of the liquid is,a)2b)3c)2.5d)1.5Correct answer is option 'D'. Can you explain this answer?.
Two identical spheres of same mass and specific gravity (which is the ratio of density of a substance and density of water) 2.4 have different charges Q and -3Q. They are suspended from two strings of same length L fixed to points at the same horizontal level, but distance L from each other. When the entire set up is transferred inside a liquid of specific gravity 0.8, it is observed that the inclination of each string in equilibrium remains unchanged. Then the dielectric constant of the liquid is,a)2b)3c)2.5d)1.5Correct answer is option 'D'. Can you explain this answer? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about Two identical spheres of same mass and specific gravity (which is the ratio of density of a substance and density of water) 2.4 have different charges Q and -3Q. They are suspended from two strings of same length L fixed to points at the same horizontal level, but distance L from each other. When the entire set up is transferred inside a liquid of specific gravity 0.8, it is observed that the inclination of each string in equilibrium remains unchanged. Then the dielectric constant of the liquid is,a)2b)3c)2.5d)1.5Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Two identical spheres of same mass and specific gravity (which is the ratio of density of a substance and density of water) 2.4 have different charges Q and -3Q. They are suspended from two strings of same length L fixed to points at the same horizontal level, but distance L from each other. When the entire set up is transferred inside a liquid of specific gravity 0.8, it is observed that the inclination of each string in equilibrium remains unchanged. Then the dielectric constant of the liquid is,a)2b)3c)2.5d)1.5Correct answer is option 'D'. Can you explain this answer?.
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