Solution: Power Delivered by Motor
Calculation
We established in Question 21 that for the minimum driving force, the velocity is $v = \sqrt{gh}$.
The total force at this velocity is:
$$ F = \mu v + \frac{\mu g h}{v} $$Substituting $v = \sqrt{gh}$:
$$ F = \mu \sqrt{gh} + \frac{\mu g h}{\sqrt{gh}} = \mu \sqrt{gh} + \mu \sqrt{gh} = 2\mu \sqrt{gh} $$The power delivered by the motor is given by $P = F \cdot v$:
$$ P = (2\mu \sqrt{gh}) \cdot (\sqrt{gh}) $$ $$ P = 2 \mu g h $$Correct Option: (d) $2\mu g h$
