Question

The length of an elastic spring is 'a' m when the tension is 4N and is 'b' m when the tension is 5N. The length in metre with the tension is 9N is

• A. $9(b-a)$
• B. $5b+4a$
• C. $5b-4a$
• D. $a+b$

Answer 1

Answer: (C)

$5b-4a$

$\text{Let the original length of spring be}xm\text{.}$

$\begin{array}{cc}\text{case}1:& F=4N\\ & F=k\left(\Delta x\right)\\ \Rightarrow & 4=k(a-x)⟶\left(1\right)\end{array}$

$\begin{array}{c}\text{Case}2:5=k(b-x)\to \text{(2)}\\ \text{solving}\left(1\right)\text{and}\left(2\right)\text{.}\\ x=5a-4b\\ k=\frac{1}{b-a}\end{array}$

$\text{case}3\text{: Now,}F=9N$

$\begin{array}{c}\text{We have to find the length}\\ \text{of spring now, let it be y(in m)}\end{array}$

$\begin{array}{cc}& \begin{array}{cc}9& =k(y-x)\\ \Rightarrow 9& =\frac{1}{b-a}(y-(5a-4b\left)\right)\\ \Rightarrow 9b-9a& =y-(5a-4b)\\ \Rightarrow & y=9b-9a+5a-4b=5b-4a\end{array}\\ & \text{Hence, answer is}C\text{.}\end{array}$