When the load on a wire is increased slowly from 1 kg wt to 2 kg wt the elongation increases from 0.2 mm to 0.3 mm. How much work is done during the extension ? `(g=9.8m//s^(2))`

Options

A. `1.96xx10^(-3)J`
B. `19.6xx10^(-3)J`
C. `0.196xx10^(-3)J`
D. `16xx10^(-3)J`

Answer

A

Explanation

`W_(2)-W_(1)=(1)/(2)(F_(2)l_(2)-F_(1)l_(1))`
`=(1)/(2) g[l_(2)m_(2)-m_(1)l_(1)]`
`=(1)/(2) g[2xx0.3 xx 10^(-3)-1xx0.2 xx 10^(-3)]`
`=(1)/(2) xx 9.8 xx 10^(-3) [ 0.6 -0.2]`
`=4.9xx10^(-3) [ 0.4]`
`=19.6 xx10^(-3)J`.