Q. It is observed that the force required to tow a boat at constant velocity is proportional to the velocity. It takes 16 HP to tow a boat at a velocity of $2\ kmh^{- 1}$. The horse power required to tow this boat at a velocity of $3\ kmh^{- 1}$ is
A) 9
B) 18
C) 36
D) 72
Explanation
(c) $P = Fv$ and $F \propto v$
$\therefore\ \ P \propto v^{2};\frac{P_{2}}{P_{1}} = \frac{v_{2}^{2}}{v_{1}^{2}}$
or $\frac{P_{2}}{16} = \frac{3 \times 3}{2 \times 2} = \frac{9}{4}$
or $P_{2} = 16\frac{9}{4}\ HP\ = \ 36\ HP$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.