Question

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

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

Answer 1

The correct option is B

5b - 4a

Let $l$ be the original length. Since the material is the same,

we have $Y=\frac{Fl}{Ax}=$ constant, where $x$ is the elongation. Therefore,

$Y=\frac{4l}{A(a-l)}=\frac{5l}{A(b-l)}=\frac{9l}{A(x-l)}$

On solving for $x$ we have,

$x=5b-4a$