Question

An elastic string has length $\beta$ when subjected to 5 N tension. Its length is a when tension 4 N. When subjected to a tension of 9 N, its length will become

• A. $9(\beta -\alpha )$
• B. $5\alpha -4\beta$
• C. $5\beta -4\alpha$
• D. $\beta -\alpha$

Answer 1

Answer: (C)

$5\beta -4\alpha$

Answer 2

: $k=$ force constant of spring = force/length. Increase in length due to force = force/ $k=\frac{F}{k}$ Original length $=L$ $\therefore$ Final length $=L+\frac{F}{k}$ $\therefore$ $\beta =L+\frac{5}{k}$ $\alpha =L+\frac{4}{k}$ $\therefore$ $\beta -\alpha =\frac{I}{k}$ ?..(i) $\therefore$ $\beta =L+5(\beta -\alpha )$ or $\beta =L+5\beta -5\alpha$ or $5\alpha -4\beta =L$ When force $=9\text{ }N,$ final length be $l$ . $l=L+\frac{9}{k}=(5\alpha -4\beta )+9(\beta -\alpha )$ $=5\alpha -4\beta +9\beta -9\alpha =5\beta -4\alpha$