A spur gate has a module of $$3mm,$$ number of teeth $$16,$$ a face width of $$36mm$$ and a pressure angle of $${20^ \circ }$$. It is transmitting a power of $$3KW$$ at $$20rev/s.$$ Taking a velocity factor of $$1.5$$ and a form factor of $$0.3,$$ the stress in the gear tooth is about

A steel bar of $$10$$ $$mm\,\, \times \,\,50\,\,mm$$ is cantilevered with two $$M12$$ bolts ($$P$$ and $$Q$$) to support a static load of $$4$$ $$kN$$ as shown in figure aside.

The resultant shear stress on rivet $$P$$ is closest to

While cooling, a cubical casting of side $$40mm$$ undergoes $$3\% ,\,\,4\% $$ and $$5\% $$ volume shrinkage during the liquid state, phase transition and solid state respectively. The volume of metal compensated from the riser is

A displacement sensor (a dial indicator) measures the lateral displacement of a mandrel on the taper hole inside a drill spindle. The mandrel axis is an extension of the drill spindle taper hole axis and the protruding portion of the mandrel surface is perfectly cylindrical. Measurement are recorded as $${R_x} = $$ maximum deflection minus minimum deflection, corresponding to sensor position at $$X$$, over one rotation.

If $${R_p} = {R_Q} > 0,$$ which one of the following would be consistent with the observation?