a circular track of radius R is banked at an angle theta a vehicle negotiate the track was moving at a speed V1) draw a diagram to show all the forces acting on the vehicle2) drive an expression for the maximum safe Speed the vehicle can have on this track take ų the relevant coefficient of friction3) with what speed should the vehicle negotiate the track to minimise the wear of its tyres
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Correct option is
C
[
cosθ−μsinθ
Rg(sinθ+μcosθ)
]
1/2
Here f is frictional force =μN
Force balancing in vertical direction- Ncosθ=mg+μNsinθ⟹N=
cosθ−μsinθ
mg
(1)
In horizontal direction- μNcosθ+Nsinθ=
R
mv
2
(2)
Solving both equations-
cosθ−μsinθ
mg
(μcosθ+sinθ)=
R
mv
2
by solving- v=
cosθ−μsinθ
Rg(sinθ+μcosθ)
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