An elastic spring has length l1 when tension in it is 4N

Question

An elastic spring has a length L₁ when tension in it is 4N. It's length is L₂ when tension in it is 5N. What is the length when tension in its 9N?

a) 5L₁-4L₂           b) 4L₁+5L₂

c)5L₂-4L₁            d) 5L₁+4L₂

Answer 1

For elastic spring, Force=-kx; Therefore 5-4=-k (L₂-L₁)  [i] and

9-4=-k(L-L₁) [ii] where L=length under tension 9N

Dividing equation [i] and [ii]

1/5=(L₂-L₁)/(L-L₁)

When we solve above equation we get 

L=5L₂-4L₁

So the correct option is (c) 5L₂-4L₁