A) Reduce the mass to one fourth
B) Quadruple the mass
C) Double the mass
D) Half the mass
Correct Answer: A
Solution :
Key Idea: Spring oscillator executes SHM. In motion of a spring oscillator the acceleration is directly proportional to displacement hence motion is SHM. It periodic time is given by \[T=2\pi \sqrt{\frac{m}{k}}\] Also frequency \[\left( n \right)=\frac{1}{T}\] \[\Rightarrow \] \[n=\frac{1}{2\pi }\sqrt{\frac{k}{m}}\] For\[{{n}_{2}}=2{{n}_{1}}\], we have \[\frac{{{n}_{1}}}{{{n}_{2}}}=\sqrt{\frac{{{m}_{2}}}{{{m}_{1}}}}\] \[\therefore \] \[\frac{{{n}_{1}}}{2{{n}_{2}}}=\sqrt{\frac{{{m}_{2}}}{{{m}_{1}}}}\] \[\Rightarrow \] \[\frac{1}{4}=\frac{{{m}_{2}}}{{{m}_{1}}}\] \[\Rightarrow \] \[{{m}_{2}}=\frac{{{m}_{1}}}{4}\] Hence, mass is reduced to one-fourth to make the frequency double.You need to login to perform this action.
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