Question

The force required to stretch a spring varies with the distance as shown in the figure. If the experiment is performed with the above spring of half the length, the line OA will:-

• A. Shift towards F−axis
• B. Shift towards X−axis
• C. Remains as it is
• D. Become double in length

Answer 1

The correct option is A

Shift towards F−axis

Explanation for the correct option:

Option (A): Shift towards F−axis

1. When the length of spring gets halved, its spring constant will become double.
2. Hence, $$\begin{gathered} \mathrm{k}\propto \frac{1}{\mathrm{x}}\propto \frac{1}{\mathrm{L}} \\ \therefore \mathrm{k}\propto \frac{1}{\mathrm{L}} \end{gathered}$$
3. Here $\mathrm{k}=$ spring constant, $\frac{1}{\mathrm{x}}=$slope of the F-X graph, and $\mathrm{L}=$length of the spring.
4. Here the slope (OA) of the force-displacement graph gives the spring constant $\left(\mathrm{k}\right)$ of spring.
5. Hence, If the experiment is performed with the above spring of half the length, k will become double and the slope of the graph increases, i.e. graph shifts towards the force-axis (OA').
6. The graph showing the Shift towards F−axis (OA') can be shown as:

Explanation for the incorrect option:

Option (B): Shift towards X−axis

1. If the length of the given spring will be halved, the value of k will be doubled, and hence the slope of the graph i.e OA will shift towards the force-axis and not towards the X−axis.
2. Hence, the given option is the incorrect one.

Option (C): Remains as it is

1. As the length of the given spring gets halved, the value of k will be doubled, and hence the slope of the graph i.e OA will increase and does not remain constant.
2. Hence, the given option does not coincide with the correct concept.

Option (D): Become double in length

1. As the length of the given spring gets halved, the value of k will be doubled, and hence the slope of the graph i.e OA will increase but it does not become double in length.
2. Thus, the given option does not represent the correct concept.

Hence, option A is correct.