CBSE Class 11-science Answered
Pls solve .
Asked by pb_ckt | 21 May, 2019, 03:03: PM
Expert Answer
If l is length of rod is l and its radius is r, then Volume V = πr2l ..........................(1)
If we take logarithm on both side of eqn.(1), then we have, ln( V ) = ln( π )+ 2ln( r ) + ln( l ) .....................(2)
If we differentiate eqn.(2), we get (dV/V) = 2(dr/r) + ( dl/l ) ...........................(3)
we rewrite eqn.(3) in terms of percentage error as, [ (dV/V)×100 ] = 2 [ (dr/r)×100 ] + [ (dl/l)×100 ] ................(4)
percentage error in radius measurement = (0.1/10)×100 = 1%
percentage error in length measurement = (1/1000)×100 = 0.1%
we get percentage error in volume from eqn.(4) as, [ (dV/V)×100 ] = 2×1 + 0.1 = 2.1%
Answered by Thiyagarajan K | 21 May, 2019, 06:12: PM
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