A) reduce the mass to one fourth
B) quadruple the mass
C) double the mass
D) half the mass
Correct Answer: B
Solution :
The frequency of spring oscillator is given by \[V=\frac{1}{2\pi }\sqrt{\frac{k}{m}}\] \[\Rightarrow \] \[V\propto \sqrt{\frac{l}{m}}\Rightarrow {{V}_{1}}=\sqrt{\frac{l}{{{m}_{1}}}}\] and \[{{V}_{2}}=\sqrt{\frac{l}{{{m}_{2}}}}\] For two cases, we have, \[\frac{{{m}_{2}}}{{{m}_{1}}}={{\left( \frac{V}{2V} \right)}^{2}}=\frac{1}{4}\] \[\Rightarrow \]\[{{m}_{2}}=\frac{{{m}_{1}}}{4}\]
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