A) 1 : 2
B) 1 : 4
C) 4 : 1
D) 2 : 1
Correct Answer: A
Solution :
When a body oscillates in simple 'harmonic motion, it is acted upon by a restoring force which tends to bring it in the equilibrium position. Due to this force there is potential energy in the body. Restoring force acting on body is F = mass \[\times \] acceleration \[=m{{\omega }^{2}}x\] where,\[\omega \]is angular frequency and \[x\] is displacement. The work done in displacing the body appears as potential energy U. \[U=W=\int_{0}^{x}{m{{\omega }^{2}}xdx=m{{\omega }^{2}}\frac{{{x}^{2}}}{2}}\] Here, mo\[m{{\omega }^{2}}=k=\] spring constant. \[\therefore \] \[{{U}_{1}}=\frac{1}{2}{{k}_{1}}{{x}^{2}},{{U}_{2}}=\frac{1}{2}{{k}_{2}}{{x}^{2}}\] \[\therefore \] \[\frac{{{U}_{1}}}{{{U}_{2}}}=\frac{1500}{3000}=\frac{1}{2}\] \[\therefore \] \[{{U}_{2}}:{{U}_{2}}=1:2\]You need to login to perform this action.
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