Question : Two persons pull a wire towards themselves. Each person exerts a force of 200 N on the wire. Young's modulus of the material of wire is 1×1011 N/m². Original length of the wire is 2 m and the area of cross section is 2 cm². The wire will extend in length by ________µm.
(A) 2
(B) 40
(C) 20
(D) 4
Doubt by Divya and Anamika
Solution :
Here
Here
F=200 N
Explaination :
Explaination :
When two people pull a wire from opposite ends with equal forces of 200 N, the wire experiences a tension of only 200 N, not 400 N. This is because the two forces act in opposite directions on different ends of the wire, keeping it in equilibrium. The tension throughout the wire equals the force applied by either person. If both forces acted on the same side in the same direction, then they would add up. But since they oppose each other, the tension is 200 N, the same as if one end were fixed and the other pulled with 200 N.
Y=1011 N/m²
L = 2m
A = 2 cm²
= 2×10-4 m²
We know,
Y=FL/AΔL
ΔL=FL/AY
ΔL=(200×2)/(2×10-4×1011)
ΔL=400/(2×107)
ΔL=200×10-7 m
ΔL=20×10-6 m
ΔL=20µm
Y=1011 N/m²
L = 2m
A = 2 cm²
= 2×10-4 m²
We know,
Y=FL/AΔL
ΔL=FL/AY
ΔL=(200×2)/(2×10-4×1011)
ΔL=400/(2×107)
ΔL=200×10-7 m
ΔL=20×10-6 m
ΔL=20µm
Hence, (C) 20, would be the correct option.