Question

A wire of length 1 m and diameter 1 mm is clamped at one of its ends then then the couple required to twist the other end by 90°. Given modulus of rigidity = 298 GPa​

Answer 1

Explanation:

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Answer 2

Answer:

Approximately 0.0043 N/m of torque is required to twist the other end of the wire by 90°.

Explanation:

We must apply the following formula to determine the couple needed to twist the wire by 90 degrees:

                                            T = G · J · ∅

Where,  T = twisting couple

G = modulus of rigidity

J = polar moment of inertia

∅ = angle of twist (in radians).

We can determine the polar moment of inertia as follows given that the wire has a diameter of 1 mm and a length of 1 m:

                                       J = (π · d⁴) / 32

                                        J = (3.14 x (0.001⁴)) / 32

                                      J = 9.865 x 10⁻⁹ m⁴

Calculation:

                                        T = G · J · ∅

                                        T = 298 · (9.865 x 10⁻⁹) · (90 x (3.14/180))

                                        T = 0.0043 N/m

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