Q. An automobile weighing 1200 kg climbs up a hill that rises 1 m in 20 s. Neglecting frictional effects. The minimum power developed by the engine is 9000 W. If $g = 10ms^{- 2}$, then the velocity of the automobile is
A) $36\ km\ h^{- 1}$
B) $54\ km\ h^{- 1}$
C) $72\ km\ h^{- 1}$
D) $90\ km\ h^{- 1}$
Explanation
(b) Minimum force $mg\sin\theta,\ $ so, minimum power is given by
$P = mg\sin{\theta\ v\ }\ $or $v = \frac{P}{mg\sin\theta}$
or $v = \frac{9000 \times 2}{1200 \times 10 \times 1}ms^{- 1} = 15ms^{- 1}$
$= 15 \times \frac{18}{5} = 54\ kmh^{- 1}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.