First slide

Oscillation motion

Question

Two springs of force constant 1000 N/m and 2000 N/m are stretched by same force. The ratio of their respective potential energies is

Easy

A

2 : 1
B

1 : 2
C

4 : 1
D

1 : 4

Solution

F = constant
$\large U\, = \,\frac{1}{2}k{x^2}\,\,But\,\,K\,\, = \,\frac{F}{x}$
$\large U\, = \,\frac{1}{2}K\frac{{{F^2}}}{{{k^2}}} = \,\frac{1}{2}\frac{{{F^2}}}{k}\,\,\,\,\,\,\,\,\,\,\,\,\,\frac{{{U_1}}}{{{U_2}}}\, = \,\frac{{{k_2}}}{{{k_1}}}\, = \,\frac{{2000}}{{1000}}\, = \,\frac{2}{1}$

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