Answer to Question #96938 in Mechanics | Relativity for Navya

Question #96938
A wire of length 2m and radius 2mm is fixed to the center of wheel a torque of magnitude 0.0395Nm is applied to twist the wire find the regidity modulus of wire if angular twist is 0.038radian
1
Expert's answer
2019-10-22T10:44:30-0400

Rigidity modulus of wire


We need to find the rigidity modulus of wire if angular twist is 0.038 radian


Solution:


Length of the wire = l = 2 m


Angular twist = θ\theta = 0.038 radians


Torque magnitude = T{T} = 0.0395 Nm


Rigidity modulus = G{G}


Torsion constant =

J=12πr4{J} =\frac { 1 } {2} \pi r^4

It depends on the radius of the radius of the wire


Here,

r=2mm=2×103mr = 2 mm = 2 \times 10^{-3} m



Plug this r in the equation of J


J=12πr4=12π(2×103)4=2.52×1011m4{J} =\frac { 1 } {2} \pi r^4 =\frac {1}{2} \pi(2 \times 10^{-3})^4 = 2.52 \times 10^{-11} m^4

We know the formula for Rigidity modulus



G=TlθJ=0.0395×20.038×2.52×1011{G} =\frac {T l} {\theta J} = \frac {0.0395 \times 2} {0.038 \times2.52\times 10^{-11}}


G=8.2×1010Nm2{G} = 8.2 \times 10^{10} \frac {N} {m^2}

Answer:

Rigidity modulus =

G=8.2×1010Nm2{G} = 8.2 \times 10^{10} \frac {N} {m^2}


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