The length of an elastic string is a metre when the longitudinal tension is 4 N and b metre when the longitudinal tension is 5 N. The length of the string in metre when the longitudinal tension is 9 N is

Options

A. `9(b-a)`
B. `5b+4a`
C. `5b-4a`
D. `a+b`

Answer

C

Explanation

`L=(T_(2)l_(1)+T_(1)l_(2))/(T_(2)-T_(1)) = (5xxa-4b)/(5-4)`
`L= 5a-4b " " `…(i)
For first and third tension,
`L=(T_(3)l_(1)l_(3))/(T_(3)-T_(1)=(9a-4l_(3))/(9-4)`
`=(9a-4l_(3))/(5) " " ` …(ii)
From equation (i) and (ii), `5a-4b=(9a-4l_(3))/(5)`
`25a-20b=9a-4l_(3)`
`25a-20b=9a-4l_(3)`
`16a-20b= -4l_(3)`
`therefore l_(3)=5b-4a`.