A rope brake dynamometer attached to the crank shaft of an $$I.C.$$ engine measures a brake power of $$10$$ kW when the speed of rotation of the shaft is $$400$$ rad/s. The shaft torque (in N-m) sensed by the dynamometer is ________

A hollow shaft of $$1$$ m length is designed to transmit a power of $$30$$ kW at $$700$$ rpm. The maximum permissible angle of twist in the shaft is $${1^0}.$$ The inner diameter of the shaft is $$0.7$$ times the outer diameter. The modulus of rigidity is $$80$$ GPa. The outside diameter (in mm) of the shaft is _______

A cantilever beam with square cross-section of 6 mm side is subjected to a load of 2kN normal to the top surface as shown in figure. The Young’s modulus of elasticity of the material of the beam is 210 GPa. The magnitude of slope (in radian) at Q (20 mm from the fixed end) is ________

A gas is stored in a cylindrical tank of inner radius $$7$$ m and wall thickness $$50$$ mm. The gage pressure of the gas is $$2$$ MPa. The maximum shear stress (in MPa) in the wall is