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 the road is negligible.

Options

A. The car cannot make a turn without skidding
B. If the car turns at a speed less than 40 km/hr, it will slip down
C. If the car turns at the correct speed of 40 km/hr the force by the road on the car is equal to `(mv^(2))/(r )`
D. If the car turns 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 `(mv^(2))/(r )`

Answer

B, D

Explanation

For exactly 40 km/hr, car will not slip,
`v = sqrt(r g tan theta)` r decreases as v decreases
`N sin theta = (mv^(2))/(r )` , `N cos theta = m g N = sqrt(((mv^(2))/(r ))^(2) + (mg)^(2))`