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Question

A metal wire of length L1 and area of cross section A is attached to a rigid support. Another metal wire of length L2 and of the same cross-sectional area is attached to the free end of the first wire. A body of mass M is then suspended from the free end of the second wire. If Y1 and Y2 are the Young's moduli of the wires respectively, the effective force constant of the system of two wires is

A
Y1Y2A2(Y1L2+Y2L1)
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B
Y1Y2A2(L1L2)1/2
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C
Y1Y2A(Y1L2+Y2L1)
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D
(Y1Y2)1/2A2(L1L2)1/2
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Solution

The correct option is C Y1Y2A(Y1L2+Y2L1)
The wires are connected in series
Y=FlAΔlYAl=FΔlk=YAl
K is spring constant
In series spring constants are added as
1K1+1K2=1Kl1Y1A+l2Y2A=1K
K=Y1Y2AY1L2+Y2L1

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