Question

A crane is used to lift $1000\, kg$ of coal from a mine $100\, m$ deep. The time taken by the crane is $1$ hour. The efficiency of the crane is $80 \% .$ If $g = 10\, ms ^{-2},$ then the power of the crane is

• A. $10^{4} W$
• B. $10^{6} W$
• C. $\frac{10^{4}}{36 \times 8} W$
• D. $\frac{10^{5}}{36 \times 8} W$

Answer 1

Answer: (D)

$\Delta U$ of coal $=m \cdot g \cdot h$
$=(1000 kg )\left(10 ms ^{-2}\right)(100 m )=10^{6} J$
Work done by crane in 1 hour $(80 \%$ efficiency)
$=\left(\frac{100}{80} \times 10^{6} J \right)$
Power $=\left(\frac{100}{80} \times 10^{6} J \right) \times \frac{1}{3600 s }=\left(\frac{10^{5}}{8 \times 36}\right) W$