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 __________________.

A drum brake is shown in the figure. The drum is rotating in anticlockwise direction. The coefficient of friction between drum and shoe is $$0.2.$$ The dimensions shown in the figure are in mm. The braking torque (in $$N.m$$) for the brake shoe is ________.

A force of $$400$$ $$N$$ is applied to the brake drum of $$0.5$$ $$m$$ diameter in a band-brake system as shown in the figure, where the wrapping angle is $${180^ \circ }$$ . If the coefficient of friction between the drum and the band is $$0.25,$$ the braking torque applied, in $$N.m$$ is

A band brake having band-width of $$80mm,$$ drum diameter of $$250mm,$$ coefficient of friction of $$0.25$$ and angle of wrap of $$270$$ degrees is required to exert a friction torque of $$1000N$$-$$m$$. The maximum tension (in $$kN$$) developed in the band is