The length of a rubber cord is `l_(1)` metre when the tension is 4N and `l_(2)` metre when the tension is 6 N. The length when the tension is 9 N, is

Options

A. `(2.5l_(2)-1.5l_(1))m`
B. `(6l_(2)-1.5l_(1))m`
C. `(3l_(2)-2l_(1))m`
D. `(3.5l_(2)-2.5l_(1))m`

Answer

A

Explanation

Let the original unstretched length be l.
`Y=("Stress")/("Strain")`
`=(T//A)/(Deltal//l)=(T)/(A)xx(l)/(Deltal)`
Now `Y=(4)/(A)(l)/((l_(1)-l))=(6)/(A)(l)/((l_(2)-l))`
`=(9)/(A)(l)/((l_(3)-l))`
`therefore 4(l_(3)-l)=9(l_(1)-l)`
`implies 4l_(3)+5l=9l_(1)...(i)`
Again, `6(l_(3)-l)=9(l_(2)-l)`
`implies 2l_(3)+l=3l_(2)...(ii)`
Solve Eqs. (i) and (ii), we obtain
`l_(3)=(2.5l_(2)-1.5l_(1))`