a cyclist cycles along the circumference of the circular horizontal plane of radius R The coefficient of friction depends upon the distance r from the center of the plane as u=uo(1-r/R) where uo=constant The centre of the circle with the center at the point along which the cyclist can have maximum speed is
33Question is not clear... what is asked..
But i think radius of circle for which velocity can be maximum... is
r=R/2
mμg=mv2/r
μ=μ0(1-r/R)
v2/r=μ0g(1-r/R)
v2=μ0gr(1-r/R)
v2=μ0g(rR-r2)
R
dv/dr=k(R-2r)
2√rR-r2
where k=√gμ0/R
dv/dr=0
R=r/2
it is for max velocity......