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Questions  

A circular road of radius R is banked for a speed v = 40 km/hr. A car of mass m attempts to go on the circular road, the friction coefficient between the tyre and road is negligible:

a
the car cannot make a turn without skidding
b
if the car runs at a speed less than 40 km/hr, it will slip up the slope
c
if the car runs at the correct speed of 40 km/hr, the force by the road on the car is equal to mv2r
d
if the car runs at the correct speed of 40 km,/hr, the force by the road on the car is greater than mg as well as greater than mv2r

detailed solution

Correct option is D

Car can make a turn without skidding at 40 km/hr. The car will slip down the slope if it runs at a speed less than 40 km/hr.N sin θ = mv2r   ⇒  N = 1sin θ(mv2r)and N cos θ = mg    ⇒ N = mgcos θ∵  sin θ and cos θ < 1So N > mg and N > mv2r

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