The length of an elastic wire is x under a tension of 5 N. Its length is y when the tension is 7 N. If the tension becomes 9 N then the length of the wire will be

Options

A. `2y - x`
B. `7x - 5y`
C. `7x + 5y`
D. `2y + x`

Answer

A

Explanation

Let L be the original length of the wire. When the tension of 5 N is applied, 5 = k [x - L]
where k is a constant and 7 = k[y - L]
`:. (5)/(7) = (x - L)/(y - L)`
`:. 5y - 5L = 7x - 7L`
`:. 2L = 7x - 5y` or `L = (7x - 5y)/(2)`
and `k = (5)/(x - L) = (5)/(x-((7x - 5y))/(2))`
`= (5 xx 2)/(2x - 7x + 5y)`
`= (10)/(5y - 5x) = (2)/(y - x)`
Suppose that the new length is z, when the tension is 9 N then,
`9 = k[z-L] :. (9)/(k) = z - L`
`:. z = (9)/(k) + L = (9(y - x))/(2) + (7x - 5y)/(2)`
`= (9y - 9x + 7x - 5y)/(2)`
`:. z = (4y - 2x)/(2) = 2y - x`