First slide

Stress and strain

Question

Two springs of equal lengths and equal cross-sectional area are made of material whose Young's modulii 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

Moderate

A

$\sqrt{3} : \sqrt{2}$
B

3:2
C

$3 \sqrt{3} : 2 \sqrt{2}$
D

9:4

Solution

We know that, $Y = FL / Al$
Force constant $k = F / l = YA / L$
So, time period T is given by
$T = 2 π \sqrt{(\frac{M}{k})} = 2 π \sqrt{(\frac{ML}{YA})}$
$∴ \frac{T_{1}}{T_{2}} = \sqrt{(\frac{Y_{2}}{Y_{1}})} = \sqrt{(\frac{3}{2})}$

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