A trenched conical pivot bearing has semi-cone angle α and the two radii are r1 and r2 respectively with r1 > r2. The coefficient of friction between the sliding surfaces is μ. For an axial thrust load of W kN, the reduction in torque due to friction (assuming uniform rate of wear) is

• A. μW(r1 + r2) cosec α
• B. \(\frac{1}{2}\mu W\left( {{r_1} + {r_2}} \right)\;cosec\;\alpha \)
• C. \(\frac{3}{2}\mu W\left[ {\frac{{{{\left( {{r_1}} \right)}^3} - {{\left( {{r_2}} \right)}^3}}}{3}} \right]cosec\;\alpha \)
• D. \(\frac{2}{3}\mu W\left[ {\frac{{{{\left( {{r_1}} \right)}^3} - {{\left( {{r_2}} \right)}^3}}}{3}} \right]cosec\;\alpha \)