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
B
3:2
C
33:22
D
3:2

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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