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Two springs with a spring constant of 400 N/m and 100 N/m are stretched in such a way that both have same potential energy. What will be the ratio of elongation in first spring to the second spring?
1. 2:1
2. 1: 2
3. 4:1
4. 1:4

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Best answer
Correct Answer - Option 2 : 1: 2

CONCEPT:

When a spring is stretched by length 'x', potential energy stored in it is given by:

\(U = {1\over 2}kx^2\)

Where k is a spring constant and x is the displacement from the mean position.

CALCULATION:

Given that both springs have the same potential energy and k1 = 400 N/m and k2 = 100 N/m

\(U_1 = U_2\)

\( {1\over 2}k_1x_1^2= {1\over 2}k_2x_2^2\)

\( {x_1^2\over x_2^2}={100 \over 400}\)

\( {x_1\over x_2}={1\over 2}\)

So the correct answer is option 2.

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