AP EAMCET · PHYSICS · Work Power Energy
A crane of efficiency \(80 \%\) is used to lift 8000 kg of coal from a mine of depth 108 m. If the time taken by the crane to lift the coal is one hour, then the power of the crane (in kW ) is
(Acceleration due to gravity \(=10 \mathrm{~m} \mathrm{~s}^{-2}\) )
- A 5
- B 4
- C 6
- D 3
Answer & Solution
Correct Answer
(D) 3
Step-by-step Solution
Detailed explanation
\(W = mgh = 8000 \times 10 \times 108 = 8640000 \text{ J}\) \(P_{\text{useful}} = \frac{W}{t} = \frac{8640000}{3600} = 2400 \text{ W}\) \(P_{\text{crane}} = \frac{P_{\text{useful}}}{\eta} = \frac{2400}{0.8} = 3000 \text{ W}\) \(P_{\text{crane}} = 3000 \text{ W} = 3 \text{ kW}\)
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