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