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A spherical ball of mass m with charge q can revolve in a vertical plane at the end of string of length l. at the centre of revolution there is a second ball with a charge identical in sign and magnitude to that of the revolving ball. what minimum horizontal velocity must be imparted to the ball in the lowest position to enable it to make a full revolution?
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A spherical ball of mass m with charge q can revolve in a vertical pla...
Analysis of the problem
The given problem involves a spherical ball of mass m with charge q revolving in a vertical plane at the end of string of length l. At the centre of revolution, there is a second ball with a charge identical in sign and magnitude to that of the revolving ball. We are required to find the minimum horizontal velocity that must be imparted to the ball in the lowest position to enable it to make a full revolution.
Solution
Step 1: Finding the gravitational force
The gravitational force acting on the revolving ball is given by:
Fg = mg
where m is the mass of the ball and g is the acceleration due to gravity.
Step 2: Finding the electrostatic force
The electrostatic force acting on the revolving ball due to the second ball at the centre is given by:
Fe = (1/4πε0) * ((q2)/l2)
where ε0 is the permittivity of free space, q is the charge on each ball and l is the length of the string.
Step 3: Finding the net force
The net force acting on the ball is the vector sum of the gravitational force and the electrostatic force. Since the electrostatic force is always directed towards the centre, the net force is given by:
Fnet = Fe - Fg
Step 4: Finding the velocity
The minimum horizontal velocity required to enable the ball to make a full revolution is given by the condition that the net force acting on the ball is always perpendicular to the string. Hence, we equate the net force to the centripetal force:
Fnet = mv2/l
where v is the velocity of the ball.
Step 5: Solving for velocity
Substituting the values of Fe and Fg from steps 1 and 2 and equating to the centripetal force, we get:
((1/4πε0) * ((q2)/l2)) - mg = mv2/l
Solving for v, we get:
v = sqrt(((1/4πε0) * ((q2)/l)) - g)
Step 6: Final answer
Hence, the minimum horizontal velocity that must be imparted to the ball in the lowest position to enable it to make a full revolution is given by the above equation.
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A spherical ball of mass m with charge q can revolve in a vertical plane at the end of string of length l. at the centre of revolution there is a second ball with a charge identical in sign and magnitude to that of the revolving ball. what minimum horizontal velocity must be imparted to the ball in the lowest position to enable it to make a full revolution?
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A spherical ball of mass m with charge q can revolve in a vertical plane at the end of string of length l. at the centre of revolution there is a second ball with a charge identical in sign and magnitude to that of the revolving ball. what minimum horizontal velocity must be imparted to the ball in the lowest position to enable it to make a full revolution? for IIT JAM 2024 is part of IIT JAM preparation. The Question and answers have been prepared according to the IIT JAM exam syllabus. Information about A spherical ball of mass m with charge q can revolve in a vertical plane at the end of string of length l. at the centre of revolution there is a second ball with a charge identical in sign and magnitude to that of the revolving ball. what minimum horizontal velocity must be imparted to the ball in the lowest position to enable it to make a full revolution? covers all topics & solutions for IIT JAM 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A spherical ball of mass m with charge q can revolve in a vertical plane at the end of string of length l. at the centre of revolution there is a second ball with a charge identical in sign and magnitude to that of the revolving ball. what minimum horizontal velocity must be imparted to the ball in the lowest position to enable it to make a full revolution?.
A spherical ball of mass m with charge q can revolve in a vertical plane at the end of string of length l. at the centre of revolution there is a second ball with a charge identical in sign and magnitude to that of the revolving ball. what minimum horizontal velocity must be imparted to the ball in the lowest position to enable it to make a full revolution? for IIT JAM 2024 is part of IIT JAM preparation. The Question and answers have been prepared according to the IIT JAM exam syllabus. Information about A spherical ball of mass m with charge q can revolve in a vertical plane at the end of string of length l. at the centre of revolution there is a second ball with a charge identical in sign and magnitude to that of the revolving ball. what minimum horizontal velocity must be imparted to the ball in the lowest position to enable it to make a full revolution? covers all topics & solutions for IIT JAM 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A spherical ball of mass m with charge q can revolve in a vertical plane at the end of string of length l. at the centre of revolution there is a second ball with a charge identical in sign and magnitude to that of the revolving ball. what minimum horizontal velocity must be imparted to the ball in the lowest position to enable it to make a full revolution?.
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