In order to increase the resistance of a given wire of unknown of uniform cross section to four times its value, a fraction of its length is stretched uniformly till the full length of the wire becoes `3/2` times the original length. What is the value of this fraction?

Options

A. `1/4`
B. `1/8`
C. `1/16`
D. `1/6`

Answer

B

Explanation

Suppose `n(lt1)` fraction of length is stretched to m times.
Then, `(1-n)l+(nl)m=1.5l`
or `nm-n=0.5`
`R=(rhol)/A=(rhol)/(V//l)(V=volume)`
`=(rhol^2)/V`
`R prop l^2` (if `V=`constant)
Now the second condition is
`(1-n)R+(nR)m^3=4R`
:.`m^2-n=3` ...........iii
Solving these two equations, we get
`n=1/8`