A) 0.25 J
B) 2.25 J
C) 6.25 J
D) 9 J
E) 25 J
Correct Answer: A
Solution :
The kinetic energy of spring mass system is \[K=\frac{1}{2}m{{\omega }^{2}}({{a}^{2}}-{{y}^{2}})\] where \[\omega =\frac{2\pi }{T}=\frac{2\pi }{2\pi }\sqrt{\frac{K}{m}}=\sqrt{\frac{K}{m}}\] Given, \[m=250\text{ }g=250\times {{10}^{-3}}kg,\] \[\omega =\sqrt{\frac{50}{250\times {{10}^{-3}}}}\] \[{{a}^{2}}-{{y}^{2}}={{10}^{-2}}\] \[\therefore \] \[K=\frac{1}{2}\times 250\times {{10}^{-3}}\times 100\times 2\times \frac{1}{100}\] \[K=0.25\,J\]
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