A metal wire of length $L_1$ and area of cross section $A$ is attached to a rigid support. Another metal wire of length $L_2$ 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 $Y_1$ and $Y_2$ are the Youngs moduli of the wires respectively, the effective force constant of the system of two wires is :
A metal wire of length $L_1$ and area of cross section $A$ is attached to a rigid support. Another metal wire of length $L_2$ 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 $Y_1$ and $Y_2$ are the Youngs moduli of the wires respectively, the effective force constant of the system of two wires is :
- A
$\frac{{\left[ {\left( {{Y_1}{Y_2}} \right)A} \right]}}{{\left[ {2\left( {{Y_1}{L_2} + {Y_2}{L_1}} \right)} \right]}}$
- B
$\frac{{\left[ {\left( {{Y_1}{Y_2}} \right)A} \right]}}{{{{\left( {{L_1} + {L_2}} \right)}^{\frac{1}{2}}}}}$
- C
$\frac{{\left[ {\left( {{Y_1}{Y_2}} \right)A} \right]}}{{\left[ {\left( {{Y_1}{L_2} + {Y_2}{L_1}} \right)} \right]}}$
- D
$\frac{{\left[ {{{\left( {{Y_1}{Y_2}} \right)}^{1/2}}A} \right]}}{{{{\left( {{L_1} + {L_2}} \right)}^{1/2}}}}$
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- [AIEEE 2009]
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