Two metal spheres, one of radius R and the other of radius 2R respectively have the same surface charge density σ. They are brought in contact and separated. What will be the new surface charge densities on them?

when spheres are kept in contact, charge redistribution takes place to get same potential. Total combined charge = 20πR2σ. Potential of both the spheres become equal, hence Q = QI2 where Q is the charge on sphere of radius R and QI is the charge on sphere of radius 2R.Thus charge on sphere of radius R becomes 20πR2σ3 , while charge on sphere of radius 2R becomes 40πR2σ3Hence new charge densities will beσ1=53σ, σ2=56σ