A factory requires an engine to lift 2000 kg of metal through a...

Work done by the engine to lift the metal is given by:

$W = mgh$

Substituting the given values ($m = 2000 \text{ kg}$, $h = 12 \text{ m}$, $g = 9.8 \text{ m/s}^2$):

$W = 2000 \times 9.8 \times 12 = 235200 \text{ J}$

The time taken is $t = 1 \text{ min} = 60 \text{ s}$.

Power $P$ is the rate of work done:

$P = \dfrac{W}{t} = \dfrac{235200}{60} = 3920 \text{ W}$

Converting the power into horsepower ($1 \text{ hp} = 746 \text{ W}$):

$P = \dfrac{3920}{746} \approx 5.25 \text{ hp}$

Using $g = 10 \text{ m/s}^2$, we get $P = \dfrac{2000 \times 10 \times 12}{60} = 4000 \text{ W}$, which gives $P = \dfrac{4000}{746} \approx 5.36 \text{ hp}$.

The closest value among the given options is $5.3 \text{ hp}$.