# The angle of twist for a transmission shaft is inversely proportional to

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The angle of twist for a transmission shaft is inversely proportional to
1. Shaft diameter
2. (shaft diameter)2
3. (shaft diameter)3
4. (shaft diameter)4

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Correct Answer - Option 4 : (shaft diameter)4

Explanation:

We know that Torsion equation is:

$\frac{{{\tau _{max}}}}{R} = \frac{{G\theta }}{L} = \frac{T}{J}$

where θ is the angle of twist, T = torque applied, L = length of the shaft, J = polar moment of inertia, d = diameter of the shaft

$J = \frac{{\pi {d^4}}}{{32}}$

From torsion equation

$\theta = \frac{{TL}}{{GJ}}$

Putting the value of ‘J’ in the above equation

$\theta = \frac{{TL}}{G} \times \frac{{32}}{{\pi {d^4}}}$

$\theta \propto \frac{1}{{{d^4}}}\;\;\;\;\;\;\;\left\{ {\because T,L\;and\;G\;are\;constant} \right\}$