When a metal wire elongates by hanging a load on it, the gravitational potential energy is decreased.

Options

A. `l Delta l`
B. `(Delta l)/(l)`
C. `(2 Delta l)/(l)`
D. `sqrt((Delta l)/(l))`

Answer

B

Explanation

Poisson's ratio `sigma= (-Delta r)/(r ) xx (l)/(Delta l)`
`(Delta r)/(r ) = - sigma (Delta l)/(l)` …(1)
Volume = Area `xx` length
`V= pi r^(2)l`
`therefore` log V = log `pi + 2 log r + log l`
`(Delta V)/(Y) = 2 (Delta r)/(r )+ (Delta l)/(l)`
`(Delta V)/(Y)= 2 ((-sigma Delta l)/(l)) + (Delta l)/(l)` (from equation 1)
`rArr (Delta V)/(V) = (Delta l)/(l) (1- 2 sigma)`
(poisson's ratio is constant for metal or material) fraction neglected poisson's ratio because we can't calcualte fraction of constant