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.