question_answer

A man is riding on a cycle with velocity 7.2 km/hr 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)             200 W

B)               175 W

C)             125 W

D)               98 W

Correct Answer: D

Solution :

            \[v=7.2\frac{km}{h}=7.2\times \frac{5}{18}=2\ m/s\]             Slope is given 1 in 20             \ \[\sin \theta =\frac{1}{20}\]                         When man and cycle moves up then component of weight opposes it motion  i.e. \[F=mg\sin \theta \]             So power of the man \[P=F\times v\]\[=mg\sin \theta \times v\]             =\[100\times 9.8\times \left( \frac{1}{20} \right)\times 2=98\ Watt\]