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Two identical charged spheres are suspended by strings of equal lengths. The strings make an angle of 30° with each other. When suspended in a liquid of density 0.8g cm–3, the angle remains the same. If density of the material of the sphere is 1.6 g cm–3 , the dielectric constant of the liquid is
- a)4
- b)3
- c)2
- d)1
Correct answer is option 'C'. Can you explain this answer?
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Two identical charged spheres are suspended by strings of equal length...
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Given Data:
- Angle between the strings = 30°
- Density of the liquid = 0.8 g/cm³
- Density of the material of the sphere = 1.6 g/cm³
Explanation:
Step 1: Equilibrium Condition
- When the spheres are suspended, the electrostatic repulsion between them balances the weight of the spheres.
- This equilibrium condition is given by the angle between the strings.
Step 2: Effect of Liquid Density
- The presence of the liquid affects the buoyant force acting on the spheres.
- The buoyant force increases with the density of the liquid.
- Since the angle remains the same, the buoyant force must have increased to balance the weight of the spheres.
Step 3: Effect of Sphere Material Density
- Since the buoyant force depends on the density of the liquid, which is equal to the density of the spheres when in equilibrium, the density of the sphere material affects the buoyant force.
- For the angle to remain the same with a higher density of the sphere material, the dielectric constant of the liquid must change.
Step 4: Determining the Dielectric Constant
- The dielectric constant of the liquid affects the electrostatic repulsion between the spheres.
- To compensate for the increased weight due to the higher density of the sphere material, the dielectric constant of the liquid must decrease.
- This decrease in dielectric constant strengthens the electrostatic repulsion between the spheres, balancing the increased weight.
Therefore, the dielectric constant of the liquid is 2 (option C) in order to maintain the equilibrium condition with spheres of higher density material.
- Angle between the strings = 30°
- Density of the liquid = 0.8 g/cm³
- Density of the material of the sphere = 1.6 g/cm³
Explanation:
Step 1: Equilibrium Condition
- When the spheres are suspended, the electrostatic repulsion between them balances the weight of the spheres.
- This equilibrium condition is given by the angle between the strings.
Step 2: Effect of Liquid Density
- The presence of the liquid affects the buoyant force acting on the spheres.
- The buoyant force increases with the density of the liquid.
- Since the angle remains the same, the buoyant force must have increased to balance the weight of the spheres.
Step 3: Effect of Sphere Material Density
- Since the buoyant force depends on the density of the liquid, which is equal to the density of the spheres when in equilibrium, the density of the sphere material affects the buoyant force.
- For the angle to remain the same with a higher density of the sphere material, the dielectric constant of the liquid must change.
Step 4: Determining the Dielectric Constant
- The dielectric constant of the liquid affects the electrostatic repulsion between the spheres.
- To compensate for the increased weight due to the higher density of the sphere material, the dielectric constant of the liquid must decrease.
- This decrease in dielectric constant strengthens the electrostatic repulsion between the spheres, balancing the increased weight.
Therefore, the dielectric constant of the liquid is 2 (option C) in order to maintain the equilibrium condition with spheres of higher density material.
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Two identical charged spheres are suspended by strings of equal lengths. The strings make an angle of 30° with each other. When suspended in a liquid of density 0.8g cm–3, the angle remains the same. If density of the material of the sphere is 1.6 g cm–3 , the dielectric constant of the liquid isa)4b)3c)2d)1Correct answer is option 'C'. Can you explain this answer?
Question Description
Two identical charged spheres are suspended by strings of equal lengths. The strings make an angle of 30° with each other. When suspended in a liquid of density 0.8g cm–3, the angle remains the same. If density of the material of the sphere is 1.6 g cm–3 , the dielectric constant of the liquid isa)4b)3c)2d)1Correct answer is option 'C'. 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 charged spheres are suspended by strings of equal lengths. The strings make an angle of 30° with each other. When suspended in a liquid of density 0.8g cm–3, the angle remains the same. If density of the material of the sphere is 1.6 g cm–3 , the dielectric constant of the liquid isa)4b)3c)2d)1Correct answer is option 'C'. 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 charged spheres are suspended by strings of equal lengths. The strings make an angle of 30° with each other. When suspended in a liquid of density 0.8g cm–3, the angle remains the same. If density of the material of the sphere is 1.6 g cm–3 , the dielectric constant of the liquid isa)4b)3c)2d)1Correct answer is option 'C'. Can you explain this answer?.
Two identical charged spheres are suspended by strings of equal lengths. The strings make an angle of 30° with each other. When suspended in a liquid of density 0.8g cm–3, the angle remains the same. If density of the material of the sphere is 1.6 g cm–3 , the dielectric constant of the liquid isa)4b)3c)2d)1Correct answer is option 'C'. 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 charged spheres are suspended by strings of equal lengths. The strings make an angle of 30° with each other. When suspended in a liquid of density 0.8g cm–3, the angle remains the same. If density of the material of the sphere is 1.6 g cm–3 , the dielectric constant of the liquid isa)4b)3c)2d)1Correct answer is option 'C'. 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 charged spheres are suspended by strings of equal lengths. The strings make an angle of 30° with each other. When suspended in a liquid of density 0.8g cm–3, the angle remains the same. If density of the material of the sphere is 1.6 g cm–3 , the dielectric constant of the liquid isa)4b)3c)2d)1Correct answer is option 'C'. Can you explain this answer?.
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