A wire is of lengths `l_(1)` and `l_(2)` when stretched by a force 4 N and 5 N respectively. Then the length of the wire when stretched by a force 7 N will be

Options

A. `3l_(2)-2l_(1)`
B. `2l_(1)-3l_(2)`
C. `7l_(1)-5l_(2)`
D. `5l_(1)-9l_(2)`

Answer

A

Explanation

For first and second tension,
`L=(T_(2)l_(1)-T_(1)l_(2))/(T_(2)-T_(1))=(5l_(1)-4l_(2))/(5-4)`
`=5l_(1)-4l_(2) " " ` …(i)
For first and third tension,
`L=(T_(3)l_(2)-T_(1)l_(3))/(T_(3)-T_(1))=(7l_(1)-4l_(3))/(7-4)`
`=(7l_(1)-4l_(3))/(3) " " ` ...(ii)
From equation (I) and (ii),
`5l_(1)-4l_(2)=(7l_(1)-4l_(3))/(3)`
`15l_(1)-12l_(2)=7l_(1)-4l_(3)`
`8l_(1)-12l_(2)=-4l_(3)`
`3l_(2)-2l_(1)=l_(3).`