In a structural member under fatigue loading, the minimum and maximum stresses developed at the critical point are $$50$$ $$MPa$$ and $$150$$ $$MPa,$$ respectively. The endurance, yield, and the ultimate strengths of the material are $$200$$ $$MPa,$$ $$300$$ $$MPa$$ and $$400$$ $$MPa,$$ respectively. The factor of safety using modified Goodman criterion is

For the brake shown in the figure, which one of the following is TRUE?

The force $${F_1}$$ and $${F_2}$$ in a brake band and the direction of rotation of the drum are as shown in the figure. The coefficient of friction is $$0.25.$$ The angle of wrap is $$3\pi /2$$ radians. It is given that $$R=1$$ $$m$$ and $${F_2} = 1N.$$ The torque (in $$N-m$$) exerted on the drum is ____________

A mass of $$2000$$ kg is currently being lowered at a velocity of $$2$$ $$m/s$$ from the drum as shown in the figure. The mass moment of inertia of the drum is $$150$$ kg-m². On applying the brake, the mass is brought to rest in a distance of $$0.5$$ $$m.$$ The energy absorbed by the brake (in $$kJ$$) is __________________.