IIT JAM Exam  >  IIT JAM Questions  >  A spherical ball of mass m with charge q can ... Start Learning for Free
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?
Most Upvoted Answer
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.
Explore Courses for IIT JAM exam
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?
Question Description
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?.
Solutions 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? in English & in Hindi are available as part of our courses for IIT JAM. Download more important topics, notes, lectures and mock test series for IIT JAM Exam by signing up for free.
Here you can find the meaning of 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? defined & explained in the simplest way possible. Besides giving the explanation of 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 detailed solution 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? has been provided alongside types of 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? theory, EduRev gives you an ample number of questions to practice 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? tests, examples and also practice IIT JAM tests.
Explore Courses for IIT JAM exam
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
10M+ students study on EduRev