A spring has a certain mass suspended from it and its period for … - Vidyadip

MCQ

A 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 is now ' $T_2$ ' The ratio $T_1 / T_2$ is

A
2
✓
$\sqrt{2}$
C
$\frac{1}{\sqrt{2}}$
D
$\frac{1}{2}$

✓

Answer

Correct option: B.

$\sqrt{2}$

(b) : When the spring cut into half, the spring constant becomes doubled.
As, $T \propto \frac{1}{\sqrt{k}} \quad \therefore \frac{T_2}{T_1}=\sqrt{\frac{k_1}{k_2}}=\sqrt{\frac{k}{2 k}} \quad \Rightarrow \frac{T_1}{T_2}=\sqrt{2}$

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