Question

The length of an elastic spring is '$a$' when tension is $4N$ and '$b$' when the tension is $5N$. The length of the spring when tensionis 9N is

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

Answer 1

The correct option is B 5b - 4a

$Y=\frac{F/A}{\Delta l/l}$

$\Delta l=\frac{Fl}{YA}$

$(a-l)=\frac{4l}{YA}$-------(1)

$(b-l)=\frac{5l}{YA}$-------(2)

Dividing (1) by (2)

$\frac{a-l}{b-l}=\frac{4}{5}$

$5a-5l=4b-bl$

$l=5a-4b$------(3)

$\Delta l=\frac{9l}{YA}$ (when force $=9N$)

$x-l=9\frac{(a-l)}{4}$ ( BY (1))

$x-l=9[a-(5a-4b\left)\right]/4$ ( BY (3))

$x=9(b-a)+l$

$=5b-4a$