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

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) 104 W (B) 106 W (C) (104/36 × 8) W (D) (105/36 × 8) W

Tardigrade Admin · Accepted Answer

Δ U of coal =m ⋅ g ⋅ h =(1000 kg )(10 ms -2)(100 m )=106 J Work done by crane in 1 hour (80 % efficiency) =((100/80) × 106 J ) Power =((100/80) × 106 J ) × (1/3600 s )=((105/8 × 36)) W

Q. A crane is used to lift $1000 k g$ 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 $g = 10 m s^{- 2},$ then the power of the crane is

$1 0^{4} W$

$1 0^{6} W$

$\frac{1 0 ^{4}}{36 \times 8} W$

$\frac{1 0 ^{5}}{36 \times 8} W$

$Δ U$ of coal $= m \cdot g \cdot h$
$= (1000 k g) (10 m s^{- 2}) (100 m) = 1 0^{6} J$
Work done by crane in 1 hour $(80%$ efficiency)
$= (\frac{100}{80} \times 1 0^{6} J)$
Power $= (\frac{100}{80} \times 1 0^{6} J) \times \frac{1}{3600 s} = (\frac{1 0 ^{5}}{8 \times 36}) W$

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

104W

106W

36×8104​W

36×8105​W