Question

What should be the power of an engine required to lift 90 metric tonnes of coal per hour from a mine whose depth is 200 m?

• A. $500W$
• B. $5000W$
• C. $500000W$
• D. $50000W$

Answer 1

The correct option is D $50000W$

Given, mass of the coal, $m=90metrictonnes=90\times 1000kg=9\times {10}^{4}kg$ ;
height through which the coal is to be lifited;
$h=200m;time,t=1h=60\times 60s=3600s$
Work done, $W=mgh$
$=(9\times {10}^4)\left(10\right)\left(200\right)=18\times {10}^{7}J$
Power, $P=\frac{W}{t}=\frac{18\times {10}^7}{3600}=50000W$