Answer to Question #96938 in Mechanics | Relativity for Navya

Question

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

Answer 1

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 = $\theta$ = 0.038 radians

Torque magnitude = ${T}$ = 0.0395 Nm

Rigidity modulus = ${G}$

Torsion constant =

$${J} =\frac { 1 } {2} \pi r^4$$

It depends on the radius of the radius of the wire

Here,

$$r = 2 mm = 2 \times 10^{-3} m$$

Plug this r in the equation of J

$${J} =\frac { 1 } {2} \pi r^4 =\frac {1}{2} \pi(2 \times 10^{-3})^4 = 2.52 \times 10^{-11} m^4$$

We know the formula for Rigidity modulus

$${G} =\frac {T l} {\theta J} = \frac {0.0395 \times 2} {0.038 \times2.52\times 10^{-11}}$$

$${G} = 8.2 \times 10^{10} \frac {N} {m^2}$$

Answer:

Rigidity modulus =

$${G} = 8.2 \times 10^{10} \frac {N} {m^2}$$