Gravitation Question 223
Question: 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) $ [2a-\frac{1}{4}a] $
D) $ [4a-3b] $
Show Answer
Answer:
Correct Answer: B
Solution:
- Let L be the original length of the wire and K be the force constant of wire. Final length = initial length + Elongation $ [L’=L+\frac{F}{K}] $ For first condition $ [a=L+\frac{4}{K}] $ (i) For second condition $ [b=L+\frac{5}{K}] $ (ii) By solving equations (i) and (ii), we get $ [L=5a-4b] $ and $ [K=\frac{1}{b-a}] $ Now when the longitudinal tension is 9 N, length of the string $ [=L+\frac{9}{K}=5a-4b+9(b-a)-5b-4a.] $
