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Two identical non-conducting solid spheres of same mass and charge are suspended in air from a common point by two non-conducting, massless strings of same length. At equilibrium, the angle between the strings is α. The spheres are now immersed in a dielectric liquid of density 800 kg m−3 and dielectric constant 21. If the angle between the strings remains the same after the immersion, then
- a)Electric force between the spheres remains unchanged
- b)Electric force between the spheres reduces
- c)Mass density of the spheres is 840 kg m−3
- d)The tension in the strings holding the spheres remains unchanged
Correct answer is option 'A,C'. Can you explain this answer?
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Two identical non-conducting solid spheres of same mass and charge are...
Let's assume that the distance between the two spheres is much larger than their radius, so that we can treat them as point charges. We can also assume that the charges are positive, since the problem does not specify their sign.
At equilibrium, the two spheres will be in electrostatic equilibrium, which means that the net electrostatic force on each sphere must be zero. This force is given by Coulomb's law:
F = k*q^2/r^2
where F is the electrostatic force, k is the Coulomb constant, q is the charge on each sphere, and r is the distance between the spheres.
Since the spheres are identical and have the same charge, the electrostatic force on each sphere will be the same. Let's call this force F_e. Since the spheres are suspended by two strings, the net force on each sphere must be the tension in the string minus the force of gravity:
F_net = T - m*g
where T is the tension in the string, m is the mass of each sphere, and g is the acceleration due to gravity.
Since the two spheres are at the same height, the net force on each sphere must be in the horizontal direction. If we resolve the forces in the horizontal and vertical directions, we get:
F_e = T*sin(theta)
m*g = T*cos(theta)
where theta is the angle between the two strings.
Dividing these two equations, we get:
tan(theta) = (F_e/m*g)
Substituting the expression for F_e from Coulomb's law, we get:
tan(theta) = (k*q^2/r^2)/(m*g)
Since the spheres have the same mass and charge, we can simplify this to:
tan(theta) = (k/r^2)*q^2/mg
Thus, the angle between the two strings is given by:
theta = atan((k/r^2)*q^2/mg)
where atan is the inverse tangent function. Note that the angle depends on the charge on the spheres, the distance between them, and the acceleration due to gravity.
At equilibrium, the two spheres will be in electrostatic equilibrium, which means that the net electrostatic force on each sphere must be zero. This force is given by Coulomb's law:
F = k*q^2/r^2
where F is the electrostatic force, k is the Coulomb constant, q is the charge on each sphere, and r is the distance between the spheres.
Since the spheres are identical and have the same charge, the electrostatic force on each sphere will be the same. Let's call this force F_e. Since the spheres are suspended by two strings, the net force on each sphere must be the tension in the string minus the force of gravity:
F_net = T - m*g
where T is the tension in the string, m is the mass of each sphere, and g is the acceleration due to gravity.
Since the two spheres are at the same height, the net force on each sphere must be in the horizontal direction. If we resolve the forces in the horizontal and vertical directions, we get:
F_e = T*sin(theta)
m*g = T*cos(theta)
where theta is the angle between the two strings.
Dividing these two equations, we get:
tan(theta) = (F_e/m*g)
Substituting the expression for F_e from Coulomb's law, we get:
tan(theta) = (k*q^2/r^2)/(m*g)
Since the spheres have the same mass and charge, we can simplify this to:
tan(theta) = (k/r^2)*q^2/mg
Thus, the angle between the two strings is given by:
theta = atan((k/r^2)*q^2/mg)
where atan is the inverse tangent function. Note that the angle depends on the charge on the spheres, the distance between them, and the acceleration due to gravity.
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Two identical non-conducting solid spheres of same mass and charge are suspended in air from a common point by two non-conducting, massless strings of same length. At equilibrium, the angle between the strings isα.The spheres are now immersed in a dielectric liquid of density 800 kg m−3and dielectric constant 21. If the angle between the strings remains the same after the immersion, thena)Electric force between the spheres remains unchangedb)Electric force between the spheres reducesc)Mass density of the spheres is 840 kg m−3d)The tension in the strings holding the spheres remains unchangedCorrect answer is option 'A,C'. Can you explain this answer?
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Two identical non-conducting solid spheres of same mass and charge are suspended in air from a common point by two non-conducting, massless strings of same length. At equilibrium, the angle between the strings isα.The spheres are now immersed in a dielectric liquid of density 800 kg m−3and dielectric constant 21. If the angle between the strings remains the same after the immersion, thena)Electric force between the spheres remains unchangedb)Electric force between the spheres reducesc)Mass density of the spheres is 840 kg m−3d)The tension in the strings holding the spheres remains unchangedCorrect answer is option 'A,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 non-conducting solid spheres of same mass and charge are suspended in air from a common point by two non-conducting, massless strings of same length. At equilibrium, the angle between the strings isα.The spheres are now immersed in a dielectric liquid of density 800 kg m−3and dielectric constant 21. If the angle between the strings remains the same after the immersion, thena)Electric force between the spheres remains unchangedb)Electric force between the spheres reducesc)Mass density of the spheres is 840 kg m−3d)The tension in the strings holding the spheres remains unchangedCorrect answer is option 'A,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 non-conducting solid spheres of same mass and charge are suspended in air from a common point by two non-conducting, massless strings of same length. At equilibrium, the angle between the strings isα.The spheres are now immersed in a dielectric liquid of density 800 kg m−3and dielectric constant 21. If the angle between the strings remains the same after the immersion, thena)Electric force between the spheres remains unchangedb)Electric force between the spheres reducesc)Mass density of the spheres is 840 kg m−3d)The tension in the strings holding the spheres remains unchangedCorrect answer is option 'A,C'. Can you explain this answer?.
Two identical non-conducting solid spheres of same mass and charge are suspended in air from a common point by two non-conducting, massless strings of same length. At equilibrium, the angle between the strings isα.The spheres are now immersed in a dielectric liquid of density 800 kg m−3and dielectric constant 21. If the angle between the strings remains the same after the immersion, thena)Electric force between the spheres remains unchangedb)Electric force between the spheres reducesc)Mass density of the spheres is 840 kg m−3d)The tension in the strings holding the spheres remains unchangedCorrect answer is option 'A,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 non-conducting solid spheres of same mass and charge are suspended in air from a common point by two non-conducting, massless strings of same length. At equilibrium, the angle between the strings isα.The spheres are now immersed in a dielectric liquid of density 800 kg m−3and dielectric constant 21. If the angle between the strings remains the same after the immersion, thena)Electric force between the spheres remains unchangedb)Electric force between the spheres reducesc)Mass density of the spheres is 840 kg m−3d)The tension in the strings holding the spheres remains unchangedCorrect answer is option 'A,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 non-conducting solid spheres of same mass and charge are suspended in air from a common point by two non-conducting, massless strings of same length. At equilibrium, the angle between the strings isα.The spheres are now immersed in a dielectric liquid of density 800 kg m−3and dielectric constant 21. If the angle between the strings remains the same after the immersion, thena)Electric force between the spheres remains unchangedb)Electric force between the spheres reducesc)Mass density of the spheres is 840 kg m−3d)The tension in the strings holding the spheres remains unchangedCorrect answer is option 'A,C'. Can you explain this answer?.
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ample number of questions to practice Two identical non-conducting solid spheres of same mass and charge are suspended in air from a common point by two non-conducting, massless strings of same length. At equilibrium, the angle between the strings isα.The spheres are now immersed in a dielectric liquid of density 800 kg m−3and dielectric constant 21. If the angle between the strings remains the same after the immersion, thena)Electric force between the spheres remains unchangedb)Electric force between the spheres reducesc)Mass density of the spheres is 840 kg m−3d)The tension in the strings holding the spheres remains unchangedCorrect answer is option 'A,C'. Can you explain this answer? tests, examples and also practice JEE tests.
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