A) reduce the mass to one-fourth
B) quadruple the mass
C) double the mass
D) half the mass
Correct Answer: A
Solution :
The frequency of spring oscillator is \[v=\frac{1}{2\pi }\sqrt{\left( \frac{k}{m} \right)}\] \[\Rightarrow \] \[v\propto \sqrt{\left( \frac{1}{m} \right)}\] Hence, \[\frac{{{v}_{1}}}{{{v}_{2}}}=\sqrt{\left( \frac{{{m}_{2}}}{{{m}_{1}}} \right)}\] or \[\frac{{{m}_{2}}}{{{m}_{1}}}={{\left( \frac{{{v}_{1}}}{{{v}_{2}}} \right)}^{2}}=\left( \frac{v}{2v} \right)=\frac{1}{4}\] \[\therefore \] \[{{m}_{2}}=\frac{{{m}_{1}}}{4}\]
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