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Question

Two springs of equal lengths and equal cross – sectional areas 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


A
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B
3: 2
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C
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D
9 : 4
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Solution

The correct option is C
Young’s modulus Y=FA.Ll
Force constant k=Fl=YAL
Where l is the extension in the spring of original length L and cross-sectional area A when a force F = Mg is applied.  Now, the time period of vertical oscillations is given by
T=2πMk=2πMLYAT1T2=Y2Y1=32
 

Physics

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