The correct option is
C 40 km/hr
Speed of vehicle (v) = 36 km/hr = 10 m/sec
Let
θ be the angle at which the road is banked.
Let us find out all the forces that are acting on this moving vehicle
(i) Mg in downward direction
(ii) N (normal reaction) acting perpendicular to the surface of road
(iii) pseudo force acting in radially outward direction
(iv) frictional force acting parallel to the road, either in inward or outward direction
Case 1:
To avoid slipping of the vehicle
In this case friction will act in outward direction
Let us now resolve all the forces in the direction along the surface and perpendicular to the surface.
Now we get ,
N=Ma sinθ+Mgcosθ.......(i)
Mgsinθ=μN+Ma cosθ...(ii)
To calculate
θ we know
tanθ=ag
tanθ=v2rg
tanθ=(10)220g = 0.5........(iii)
Put (iii) in (ii) and (i) we get
Vmin=10√6 m/s = 14.7 km/h
Case 2:
To avoid vehicle from skidding up
In this case friction will act inward direction.
Again resolve the forces along the surface and perpendicular to the surface.
μN+mg sinθ=ma3 cosθ.......(v)
N=ma3 sinθ+mg cosθ.....(vi)
a3=v2maxr...(vii)
on solving (v), (vi) and (vii) this we get
vmax= 44.1 km/h
∴ Options A, B and C are correct