A weightless spring which has a force constant oscillates with frequency $n$ when a mass $m$ is suspended from it. The spring is cut into two equal halves and a mass $2m $ is suspended from it. The frequency of oscillation will now become
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(a) $n = \frac{1}{{2\pi }}\sqrt {\frac{k}{m}} $
==>$\frac{n}{{n'}} = \sqrt {\frac{k}{m} \times \frac{{m'}}{{K'}}} $
$ = \sqrt {\frac{k}{m} \times \frac{{2m}}{{2K}}} = 1$
==> $n' = n$
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