The correct option is A 46.74 m/s, 29.39 m/s
Given: radius of curve = r=500 m, Angle of banking =θ=10∘,
and coefficient of friction =μ=0.25,g=9.8 m/s2,
To find safe velocity = v=?, To avoid wear and tear, vsp=?
Maximum speed to avoid slipping:
In this case, centripetal force is provided by horizontal component of both normal reaction and friction (i.e there will be wear and tear)
vmax=√rg(tanθ+μs)(1−μstanθ)
=√500×9.8(tan10∘+0.25)(1−0.25tan10∘)
=√4900(0.1763+0.25)(1−0.25×0.1763)=√4900(0.4263)1−0.0441=√20890.9559
∴vmax=√2185=46.74 m/s
Maximum speed to avoid wear and tear:
In order to avoid wear and tear, centripetal force for making the turn has to provided by the horizontal component of normal reaction alone. (i.e no friction)
vopt=√rgtanθ=√500×9.8×tan10∘
=√500×9.8×0.1763=29.39 m/s