# The external and internal radii of the frictional faces in clutch are 100 mm and 60 mm, respectively. Determine the mean radius of friction face assum

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The external and internal radii of the frictional faces in clutch are 100 mm and 60 mm, respectively. Determine the mean radius of friction face assuming the uniform pressure condition.
1. 60 mm
2. 70 mm
3. 82 mm
4. 78 mm

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Correct Answer - Option 3 : 82 mm

Concept:

The mean radius of friction face assuming the uniform pressure condition is given by:

${R_m} =\frac{2}{3}\left( {\frac{{r_o^3\; - \;r_i^3}}{{r_o^2\; - \;r_i^2}}} \right)$

Where ro & ri are the external and internal radii of the clutch.

Calculation:

Given:

ro = 100 mm, ri = 60 mm.

${R_m} =\frac{2}{3}\left( {\frac{{r_o^3\; - \;r_i^3}}{{r_o^2\; - \;r_i^2}}} \right)$

${R_m} =\frac{2}{3}\left( {\frac{{100^3\; - \;60^3}}{{100^2\; - \;60^2}}} \right) = 81.67\; mm$ ≈ 82 mm

∴ The mean radius of the friction face assuming the uniform pressure condition is 82 mm.