question_answer

A man is riding on a cycle with velocity 7.2 km/h up a hill having a slope 1 in 20. The total mass of the man and cycle is 100 kg. The power of the man is

A)  98 W                                    

B)  125 W

C)  175 W                                  

D)  200 W

Correct Answer: A

Solution :

                Given, \[v=7.2\,km{{h}^{-1}}\] \[=7.2\times \frac{5}{18}=2\,m\text{/}s\] Slope is given 1 in 20 i.e,          \[\sin \theta =\frac{1}{20}\] For the upward motion to the cyclist. \[F=mg\,\sin \theta \] \[\therefore \] Power of the man, \[P=F\times v=mg\,\sin \theta \times v\] \[=100\times 9.8\times \frac{1}{20}\times 2=98\,W\]