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CBSE Class 12-science Answered

Two metal spheres of radii R and 2R having charges 2Q and Q are touched with each other and separated. Final charge on them are in the ratio of ? a) 1:2 b) 2:5 c) 2:3 d) 3:4
Asked by arunavamitra50 | 16 May, 2019, 12:18: PM
answered-by-expert Expert Answer
Let Q1 be the charge on sphere-1 whose radius is R,  when the two charged spheres are in contact.
 
Let Q2 be the charge on sphere-2 whose radius is 2R,  when the two charged spheres are in contact.
 
By conservation of charge, Q1 + Q2 = 3Q  ..............(1)
 
when two charges are in contact their potenials are same.
 
hence we have,    begin mathsize 12px style fraction numerator Q subscript 1 over denominator 4 πε subscript 0 space straight R end fraction space equals space fraction numerator Q subscript 2 over denominator 4 πε subscript 0 space 2 straight R end fraction space space space o r space space space space Q subscript 1 space space equals space fraction numerator begin display style Q subscript 2 end style over denominator begin display style space 2 end style end fraction space space......... left parenthesis 2 right parenthesis end style
By solving (1) and (2), we get Q1 = Q   or   Q2 = 2Q
 
Hence charges in the spheres are in the ratio 1:2
Answered by Thiyagarajan K | 16 May, 2019, 01:21: PM

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