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 ?

Efficiency of motor = 90 %

As we know that :

$efficiency=\frac{outputpower}{inputpower}$ ...........(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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