Question
A conducting sphere of radius R carries a charge Q. If
half of the charge is transferred to an identical uncharged sphere brought into contact and removed, the electrostatic energy of the system becomes:Solution
The electrostatic energy (U) of a charged conducting sphere is given by: 
When the charged sphere (with charge Q) is brought into contact with an identical uncharged sphere, the charge will be equally distributed between them due to their identical nature and conducting property.
- Each sphere will have a charge of Q/2.
So, the final electrostatic energy of the system is half of the original electrostatic energy. Therefore, the correct answer is (a) Half of original.
I: x2 - 33x + 242 = 0
II: y2 - 4y - 77 = 0
I. 2y2 + 11y + 15 = 0
II. 3x2 + 4x - 4= 0
I. 14p2 – 135p + 81 = 0
II. 7q2 – 65q + 18 = 0
I. 2x² - 7x + 3 = 0
II. 8y² - 14y + 5 = 0
What will be the product of smaller roots of both equations.
I. 144x² - 163x - 65 = 0
II. 91y² - 128y -48 = 0
Quantity I: A vessel contains a mixture of milk and water in the ratio of 7 : 5. If 9 litre of mixture is sold and replaced by same amount of water then...
I. 8x – 3y = 85
II. 4x – 5y = 67
I. p² - 10p +21 = 0
II. q² + q -12 = 0
Solve the quadratic equations and determine the relation between x and y:
Equation 1: 4x² - 12x + 9 = 0
Equation 2: 2y² + 8y + 6 = 0
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