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Question: A force of 200 N is applied at one end of a wire of length 2 m and having area of cross-section \(10...

A force of 200 N is applied at one end of a wire of length 2 m and having area of cross-section 10−2 cm210 ^ { - 2 } \mathrm {~cm} ^ { 2 }. The other end of the wire is rigidly fixed. If coefficient of linear expansion of the wire α=8×10−6/∘C\alpha = 8 \times 10 ^ { - 6 } / { } ^ { \circ } \mathrm { C } and Young's modulus

Y=2.2×1011 N/m2Y = 2.2 \times 10 ^ { 11 } \mathrm {~N} / \mathrm { m } ^ { 2 } and its temperature is increased by 5°C, then the increase in the tension of the wire will be

A

4.2 N

B

4.4 N

C

2.4 N

D

8.8 N

Answer

8.8 N

Explanation

Solution

Increase in tension of wire=YAαΔθ= Y A \alpha \Delta \theta

=8×10−6×2.2×1011×10−2×10−4×5=8.8 N= 8 \times 10 ^ { - 6 } \times 2.2 \times 10 ^ { 11 } \times 10 ^ { - 2 } \times 10 ^ { - 4 } \times 5 = 8.8 \mathrm {~N}