Question

The input power to an electric motor is 200 kW. Its efficiency is 80 %. It operates a crane of efficiency 90 %. If the crane is lifting a load of 3.6 tonnes, the velocity with which the load moves is

• A. $8m{s}^{-1}$
• B. $4m{s}^{-1}$
• C. $2m{s}^{-1}$
• D. $40m{s}^{-1}$

Answer 1

Answer: (B)

$4m{s}^{-1}$

Power with which crane lifts the load $=0.8\times 0.9\times$ input power

$P=0.8\times 0.9\times 200kW$

Now, $P=\overrightarrow{F}.\overrightarrow{v}$

Here, $F=mg$ (since there is no acceleration)

${10}^3\times 0.8\times 0.9\times 200=3.6\times {10}^3\times 10\times v$

$\Rightarrow v=4m/s$