A man cycling up a smooth inclne road, climbs the road at a constant spped of 2m/s. The total mass of the man and the cycle is 150 kg and the inclination of the road with the horizonal is `30^(@)`. What is the minimum horse power spend by the man?
[Take `g=10m//s^(2)` and 1 horse power `=750` watt]

Options

A. 1.25H.P
B. 1.5H.P
C. 2H.P
D. 5H.P

Answer

C

Explanation

`because F prop S^(-1//3) " " therefore m xx a prop S^(-1//3) " or" a prop S^(-1//3)`
But `a=(dv)/(dt)=(dv)/(dS)xx(dS)/(st)=v(dv)/(dS)`
`therefore vdv prop S^(-1//3)dS`
On integrating, we get `int vdv prop int S^(-1//3)dS`
`v^(2)prop S^(2//3)` or `v prop S^(1//3)`
But Power = Force `xx` velocity
`therefore P prop S^(-1//3)` or `P prop S^(0)`
Thus power does not depend upon S.