A) 1.5
B) 3.2
C) 0.5
D) 2.1
Correct Answer: C
Solution :
Key Idea: In first set up, the springs are joined in parallel and in second, the springs are joined in series. When springs are connected in parallel, the effective spring constant is \[{{k}_{1}}=k+k=2\,k\] Hence, time period \[{{T}_{1}}=2\,\pi \sqrt{\frac{M}{{{k}_{1}}}}=2\pi \sqrt{\frac{M}{2\,k}}\] ... (i) When springs are connected in series, the effective spring constant is \[\frac{1}{{{k}_{2}}}=\frac{1}{k}+\frac{1}{k}=\frac{2}{k}\] \[\Rightarrow \] \[{{k}_{2}}\frac{k}{2}\] Therefore, time period, \[{{T}_{2}}=2\pi \sqrt{\frac{M}{{{k}_{2}}}}\] \[=2\pi \sqrt{\frac{M}{k/2}}\] \[{{T}_{2}}=2\pi \sqrt{\frac{2M}{k}}\] ... (ii) Dividing Eq. (i) by Eq. (ii), we have \[\frac{{{T}_{1}}}{{{T}_{2}}}=\sqrt{\frac{M/2k}{2M/k}}=\sqrt{\frac{1}{4}}=\frac{1}{2}=0.5\]You need to login to perform this action.
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