Which of the following gear tooth failures is/are induced when maximum Hertz contact stress on gear tooth surface exceeds surface endurance strength of tooth?

A bevel gear has pitch circle diameters of pinion and gear as 20 mm and 40 mm respectively. What is the face width of bevel gear?
(m =module)

A bevel gear consists of steel pinion and cast iron gear having pitch line velocity of 10 m/s. The maximum tangential force acting on the gear is 1500 N and face width is 40 mm. What is the dynamic load acting on this single stage bevel gear box if sum of errors on meshing teeth is 10 x 10^-3 N/mm? (Use Buckingham’s equation)

A straight bevel gear is manufactured by cutting process and maximum tangential force of 12000 N acts on it. What is the effective load acting between meshing teeth if pitch line velocity is 130 m/s?

A simply supported beam carries uniformly distributed load of 20 kN/m over the length of 5 m. If flexural rigidity is 30000 kN.m², what is the maximum deflection in the beam?

Torque and bending moment of 100 kN.m and 200 kN.m acts on a shaft which has external diameter twice of internal diameter. What is the external diameter of the shaft which is subjected to a maximum shear stress of 90 N/mm²?