A) \[2:1\]
B) \[1:2\]
C) \[4:1\]
D) \[1:4\]
Correct Answer: B
Solution :
Key Idea: In first set up, the springs are joined in series and in second, the springs are joined in parallel. When springs are connected in series the effective spring constant is \[\frac{1}{k}=\frac{1}{k}+\frac{1}{k}=\frac{2}{k}\] \[\Rightarrow \] \[k'=\frac{k}{2}\] Hence, frequency\[n'=\frac{1}{2\pi }\sqrt{\frac{k'}{m}}\] \[=\frac{1}{2\pi }\sqrt{\left( \frac{k}{2m} \right)}\] ? (i) When springs are connected in parallel, the effective force constant is \[k'\,\,'=k+k=2k\] Therefore, frequency is \[n'\,\,'=\frac{1}{2\pi }\sqrt{\frac{2k}{m}}\] ? (ii) Dividing Eq. (i) by Eq. (ii), we get \[\frac{n'}{n'\,\,'}=\frac{\sqrt{(k/2m)}}{\sqrt{(2k/m)}}=\frac{1}{2}\]
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