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

Answer

b

Explanation

Let L is the original length of the wire and k is force constant of wire.
final length initial + elongation
`L' = L + (F)/(K)`
for first conditon, `a = L + (4)/(k)`
For second condition, `b = L + (5)/(k)`
by solving Eqs. (i) and (ii) we get ltbr L = 5a - 4b and `k = (1)/(b -a)`
Now, when the longitudinal tension is 9 N.
Length of the string `= L + (9)/(k) = 5a - 4b + 9 (b -a) = 5b - 4a`