Question

A crane is used to lift $1000$ kg of coal from a mine $100m$ deep. If the time taken by the crane is $1$ hour, find the power of the crane assuming its efficiency to be $80$%

• A. $2403watt$
• B. $256.7watt$
• C. $346.8watt$
• D. $376.1watt$

Answer 1

Answer: (C)

$346.8watt$

Given that
$m=1000Kg$
$h=100m$
$t=1hour=60\times 60s=3600s$
$\eta =80$%
We have
$P=\frac{mgh}{t}$
$P=\frac{\left(1000\right)\left(10\right)\left(100\right)}{3600}$
$P=0.02778\times {10}^4=277.8W$
Now power of crane is
$P^{\prime }=P\times \frac{1}{\eta }$
$P^{\prime }=277.8\times \frac{100}{80}=346.8W$