A cylindrical metal rod of radius R carries a current I. The velocity of free electrons drifting at a distance r(< R) from the axis of the rod is given by  v=v01+rR where v0 is a constant. The average drift velocity of the electrons drifting in the rod is

Consider a small element of thickness dr at a distance r from the axis of the rod as shown in Fig.The current flowing through the element isdI=en dA v=en×2πrdr×v01+rR=2πenv0RRrdr+r2drIntegratingI=2πenv0RR∫0R rdr+∫0R r2dr=2πenv0RR32+R33=en⁡πR2v053I= en A×5v03Comparing with I=enA vd, we get                      vd=5v03, which is choice (d).