A uniform spring has a certain mass suspended from it and its period for vertical oscillations is $T_{1}$ . The spring is now cut into two equal halves and the same mass is suspended from one of the halves. The period of vertical oscillations now is $T_{2}$ . The ratio $\frac{T_{2}}{T_{1}}$ is

\frac{1}{2}

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\frac{1}{\sqrt{2}}

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\sqrt{2}

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Solution

The correct option is B $\frac{1}{\sqrt{2}}$
If a spring of force constant k is cut into two equal halves, the force constant of each half becomes 2k. Hence the correct choice is (b).

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