A machine of efficiency 8% is used to raise a body of mass 75kg through a vertical height of 3m in 30s. Calculate the power input. (g = 10ms-2)

Answer Details

Efficiency of a machine is defined as the ratio of output work to the input work. Mathematically, efficiency = (output work / input work) x 100%. In this question, the machine has an efficiency of 8%, which means that only 8% of the input work is converted into useful work. The rest is lost as heat or other forms of energy. Therefore, the output work of the machine is 8% of the input work. The machine is used to raise a body of mass 75kg through a vertical height of 3m in 30s. The work done by the machine is equal to the gravitational potential energy gained by the body. The gravitational potential energy gained by an object of mass m raised through a height h is given by the formula mgh, where g is the acceleration due to gravity. Therefore, the work done by the machine is W = mgh = 75 x 10 x 3 = 2250 J. We are asked to calculate the power input, which is the rate at which work is done by the machine. Power is given by the formula power = work done / time taken. Substituting the values, we get power = 2250 / 30 = 75 W. However, this is the output power of the machine. We need to calculate the input power, which is the power required to produce this output power, taking into account the efficiency of the machine. The input power is given by the formula input power = output power / efficiency. Substituting the values, we get input power = 75 / 0.08 = 937.5 W. Therefore, the power input is approximately 937.5 W, which is closest to option D: 93.8 W.