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Question

Two springs of equal lengths are equal cross-sectional areas are made of materials whose Young's moduli are in the ratio of $$2:3$$. They are suspended and loaded with the same mass. When stretched and released, they will oscillate with time periods in the ratio of?


A
9:4
loader
B
3:2
loader
C
33:22
loader
D
3:2
loader

Solution

The correct option is D $$\sqrt{3}:\sqrt{2}$$
As we know ,
$$T=2\pi \sqrt{\dfrac{m}{k}}$$
now as we know 
$$k\propto Y$$
so,
$$T\propto {\dfrac{1}{\sqrt Y}}$$
then,
$$\dfrac{T_1}{T_2}=\dfrac{\sqrt{Y_2}}{\sqrt{Y_1}}$$

$$\dfrac{T_1}{T_2}=\dfrac{\sqrt{3}}{\sqrt{2}}$$
hence option D is correct.


Physics

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