Question

When a spring is stretched by 10 cm, the potential energy stored is E. When the spring is stretched by 10 cm more, the potential energy stored in the spring becomes:
A. 2 E
B. 4 E
C. 6 E
D. 10 E

Answer 1

Hint: In this question we are asked to calculate the potential energy of the spring when it is further stretched by 10 cm. Now, the potential energy of the spring depends directly on the square of stretched distance (extension). Therefore, we will be using this to calculate the potential energy of spring when it is stretched by 20 cm.
Formula used:
\[E=\dfrac{1}{2}k{{x}^{2}}\]

Complete answer:
It is given that initially the spring was stretched by 10 cm. Later, the spring was further stretched by 10 cm more, making the total extension 20 cm.
Now it is given that the potential energy of the spring when it is stretched by 10 cm is E.
Therefore,
\[E=\dfrac{1}{2}k{{x}^{2}}\] …….. (1)
Where x = 10 cm.
Now, the potential energy if spring when the is stretched 20 cm i.e. \[2x\]is given by,
\[E'=\dfrac{1}{2}k{{(2x)}^{2}}\]
Therefore,
\[E'=\dfrac{1}{2}k{{x}^{2}}\times 4\]
But from (1) we can say that,
\[E'=E\times 4\]
Therefore,
\[E'=4E\]

So, the correct answer is “Option B”.

Note:
The energy that is stored or conserved in an object is called potential energy. This energy is dependent on the position of the object. In case of a spring, the energy that is stored in spring when it is compressed or stretched is the potential energy. It depends on the compression or expansion distance and the material of spring and number of turns. The spring constant is measured in Newtons per metre. The spring constant represents the stiffness of the spring.