An object of mass m is slowly pushed some partway up a verticle up a verticle loop ending at a point a height `h lt R` above the bottom. The coefficient of friction between the object and the track is a constant mu. Find work that has to be done against friction.

Options

A. `2mumg(2hR-h^(2))^(1//2)`
B. `mumg(hR-2h^(2))^(1//2)`
C. `4mumg(2hR-h^(2))^(1//2)`
D. `mumg(2hR-h^(2))^(1//2)`

Answer

D

Explanation

WD `=underset0overset(theta_(0))intmumgcosthetaR d theta`
`=mumgRsin theta_(0)`
`=mumg[R^(2)-(R-h)^(2)]^(1//2)`
`=mumg[2Rh-h^(2)]^(1//2)`