Assuming the drops to be spherical, 27 identical drops of mercury are charged simultaneously to the same potential of 20 volt . If all the charged drops are made to combine to form one big drop, then potential of big drop will be

Step-by-step solution

Given n = 27 small drops, each with radius r and charge q , forming a single large drop with radius R and charge Q , with the potential of a small drop given as V_ small = 20 , V . Volume conservation requires n 4 3 r^3 = 4 3 R^3 , or 27r^3 = R^3 . Taking the cube root yields R = 3r . Charge conservation gives Q = nq = 27q . The potential of a spherical drop is V = kq r for small drops, so 20 = kq r . For the large drop, V_ big = kQ R . Substituting Q = 27q and R = 3r , V_ big = k(27q) 3r = 9 kq r = 9 20 = 180 , V