A steel and brass wire, each of length 50 cm and cross-sectional area 0.005 cm2 hang from ceiling and are 15 cm apart. Lower ends of the wires are attached to a light horizontal bar.
A steel and brass wire, each of length 50 cm and cross-sectional area 0.005 cm2 hang from 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 wire extends in length by 0.1 cm. At what distance from the steel wire the load must be applied?
- a. 75 cm
- b. 5 cm
- c. 10 cm
- d. 3 cm
1 answer
@admin Given:-
Length of steel and Brass wire each =50 cm.
Cross-sectional area = 0.005 cm2
Distance between the wires = 15 cm.
Extension in wire = 0.1 cm.
(Ys) Young's modulus of steel = 2×1012 dynes/cm2
(Yb) Young's modulus of brass = 1×1012 dynes/cm2
As we know that Young's modulus is given by
Y = stress/strain
Stress = force/area
Strain = change in length/original length
Y = [F/A]/[∆l/l]
⇒ F = YA∆l/l
∵ A, ∆l and l are same for both the wires.
Taking moments about point A
Fs(x) = Fb(15-x)
Ys(x) = Yb(15-x)
Putting values of Ys and Yb
2×1012 (x) = (1×1012) (15-x)
2x = (15 – x)
3x = 15
x = 5cm.