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Question

A uniform steel wire of cross-sectional area 0.20 mm2 is held fixed by clamping its two ends. Find the extra force exerted by each clamp on the wire if the wire is cooled from 100C to 0C. Young's modulus of steel = 2.0 × 1011 N/m2. Coefficient of linear expansion of steel = 1.2 × 105/C.


A
500 N
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B
480 N
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C
4.8 N
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D
48 N
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Solution

The correct option is D 48 N

When the wire cools down the length of the wire should decrease. But as it is clamped, the length remains the same. This creates a strain in the wire, thereby stressing it.

Let, l100 and l0 be the lengths at 100C and 0C respectively. We know -

L100 = L0(1+100α).

At 0C, the unstrained length would be l0.

But, the strained length is l100 (which is constant because of the clamping).

Strain = [l100l0l0] = 100α. Also, stress = (Young's modulus) × strain.

T (the extra tension developed = force at the clamps) = stress × area,

T = 2 × 1011 × 1.2 × 105 × 100 × 6.2 × 106 N

T = 48 N.


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