The potential energy of a long spring when stretched by 2 cm is U. If the spring is stretched by 8 cm, potential energy stored in it will be :

The correct answer is Option 4. Full mathematical solution steps and hints are accessible in the interactive StemCET workspace.

Physics Q6 – NEET-UG 2023

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Home Physics Work, Energy & PowerQuestion #653

The potential energy of a long spring when stretched by

2 cm

U

. If the spring is stretched by

8 cm

, potential energy stored in it will be :

Clue 1 of 3: Elastic Potential Energy

The potential energy stored in a spring is related to its extension or compression.

🥷

Ninja Strategy•Square Proportionality

Recognize that elastic potential energy is proportional to the square of the extension. If extension increases by a factor of 'n', energy increases by 'n^2'.

🧠 Full Solution Path

Step 1: Recall the formula for elastic potential energy✦ Active

The potential energy ( $U$ ) stored in a spring is directly proportional to the square of its extension ( $x$ ) or compression. The formula is:

U = \frac{1}{2} k x^{2}

where $k$ is the spring constant.

Step 2: Set up the initial condition○ Expand

Given that when the spring is stretched by $x_{1} = 2 cm$ , the potential energy is $U_{1} = U$ . Using the formula:

U = \frac{1}{2} k (2 cm)^{2} = \frac{1}{2} k (4 {cm}^{2}) \dots (1)

Step 3: Calculate the potential energy for the new extension○ Expand

When the spring is stretched by $x_{2} = 8 cm$ , let the new potential energy be $U_{2}$ . Using the formula again:

U_{2} = \frac{1}{2} k (8 cm)^{2} = \frac{1}{2} k (64 {cm}^{2}) \dots (2)

Now, divide equation (2) by equation (1):

\frac{U_{2}}{U} = \frac{\frac{1}{2} k (64 {cm}^{2})}{\frac{1}{2} k (4 {cm}^{2})} = \frac{64}{4} = 16

Therefore, $U_{2} = 16 U$ .

💡 Teacher's Secret Hint

Notice that the units of extension (cm) cancel out in the ratio, so conversion to meters is not strictly necessary for this problem, but it's good practice for other calculations.

✦ STEM Console utilizes AI models to generate step-by-step explanations and math clues. AI can make mistakes.

Physics Question 6 – NEET-UG 2023

Clue 1 of 3: Elastic Potential Energy

🧠 Full Solution Path