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 \[\upsilon =\frac{1}{2\pi }\sqrt{\frac{k}{m}}\] \[\Rightarrow \] \[\upsilon \propto \sqrt{\frac{1}{m}}\] Hence, \[\frac{{{\upsilon }_{1}}}{{{\upsilon }_{2}}}\propto \sqrt{\frac{{{m}_{2}}}{{{m}_{1}}}}\] Or \[\frac{{{m}_{1}}}{{{m}_{2}}}={{\left( \frac{{{\upsilon }_{1}}}{{{\upsilon }_{2}}} \right)}^{2}}\] \[={{\left( \frac{{{\upsilon }_{1}}}{{{\upsilon }_{2}}} \right)}^{2}}=\frac{1}{4}\] \[{{m}_{2}}=\frac{{{m}_{1}}}{4}\]
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