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  4. A steel and a brass wire, each of length 50 cm and cross-sectional area 0.005 cm 2 hang from a ceiling and are 15 cm apart. Lower ends of the wires are attached to a light horizontal bar. A suitable downward load is applied to the bar so that each of the wires extends in length by 0.1 cm. At what distance from the steel wire the load must be applied? [Young's modulus of steel is 2 × 1012 dynes/cm 2 and that of brass is 1 × 1012 dynes / cm 2 ]

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Q. A steel and a brass wire, each of length $50 \,cm$ and cross-sectional area $0.005 \,cm ^{2}$ hang from a ceiling and are $15 \, cm$ apart. Lower ends of the wires are attached to a light horizontal bar. A suitable downward load is applied to the bar so that each of the wires extends in length by $0.1 \,cm$. At what distance from the steel wire the load must be applied?
[Young's modulus of steel is $2 \times 10^{12}$ dynes/cm $^{2}$ and that of brass is $1 \times 10^{12}$ dynes $/ cm ^{2}$ ]

WBJEEWBJEE 2020

Solution:

image
At equilibrium, Taking torque about point O
$T_{1} x=T_{2}(15-x) $
$\Rightarrow Y_{1} x=Y_{2}(15-x) $
${\left[Y=\frac{T}{A} \times \frac{L}{l} ; T \propto Y\right]}$
$1 \times 10^{12} x=2 \times 10^{12}(15-x) ; 3 x=15,$
So, $x=5\, cm$