Question

what couple must be applied to a wire 1m long,1mm diameter in order to twist one end of it through 90° ,the other end remaining fixed?n=2.8×10¹¹dynes per cm²​

Answer 1

Answer:

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Answer 2

Step-by-step Explanation:

Given: Length L = 1 m, Diameter D = 1 mm, Angle θ = 90°, coefficient of rigidity of a material n = 2.8×10¹¹ dynes/cm²​

To Find: the couple (C) applied to the wire

Solution:

• Calculating the couple that must be applied to the wire

The twisting couple of the cylinder or wire is given by,

$C = \frac{\pi n R^4}{2L} \theta = \frac{\pi n (D/2)^4}{2L} \theta$

Substituting the given values to the above formula, we get,

$C = \frac{\pi (2.8 \times 10^{11}) (0.1/2)^4}{2 \times 100} (\frac{\pi}{2}) = 4.318 \times 10^{4} \ \text{dyne cm}$

Hence, the couple that must be applied to the wire is$C = 4.318 \times 10^{4} \ \text{dyne cm}$