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

Options

A. a-b
B. 5b-4a
C. `2b- 1/4`
D. 4a-3b

Answer

B

Explanation

`T_(1)/T_(2) = (a-1)/(b-1)` [`because ` Tension,` tpropto "elongation"`]
`implies 4/5 = (a-1)/(b-1)`
At tension, T=9N is at length 'x'
`(T_(1))/(T_(3) = 9a-1)/(b-1)`
`4/9 = (a-(5a-4b))/(x-(5a-4b)) = (-4a + 4b)/(x-(5a-4b))`
`x=-9a + 9b + 5a + 4b`
`therefore x= 5b - 4a`