A motor having an efficiency Of 90 % operates a crane having an efficiency of 40%. With what constant speed does the crane lift a 500kg weight if the power supplied to the motor is 5 KW ?

Given, input power of motor = 5 kW = 5000 W
Efficiency of motor = 90 %
As we know that :
$efficiency = \frac{output power}{input power}$     ...........(1)
Therefore, output power of motor = 5000 X 90/100 = 4500 W
This output power of motor will act as input power for the crane.
Therefore, input power of crane = 4500 W
​Given, efficiency of crane = 40%
Hence, output power of crane = 4500 X 40/100 = 1800 W    (using eq. 1)
As we know that :
Power = Force X velocity
Therefore, 1800 = mg X velocity
                 1800 = 500 X 9.8 X velocity
On solving, we get :
velocity = 0.36 m/s.

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