The endurance limit of a specific grade of steel is same as its yield strength. The ultimate strength of this grade of steel is twice of its yield strength. A component made of this steel is loaded in tension and unloaded periodically. It is required that the component does NOT fail for at least $10^6$ loading cycles, as per the Soderberg law. Considering a factor of safety of 2 , the maximum applied tensile principal stress is

A pair of spur gears is required to maintain a velocity ratio of $1: 2$. The module of the gears is 10 mm and the addendum is 10 mm . If the operating pressure angle is $15^{\circ}$, the minimum number of teeth required on the pinion to ensure NO interference/undercutting is _________ (answer in integer).

Two plates of thickness 10 mm each are to be joined by a transverse fillet weld on one side and the resulting structure is loaded as shown in the figure below.

If the ultimate tensile strength of the weld material is 150 MPa and the factor of safety to be used is 3 , the minimum length of the weld required to ensure that the weld does NOT fail is __________ mm (rounded off to 2 decimal places).