question_answer

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 co-efficient 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 \[m{{v}^{2}}/r\]

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 \[m{{v}^{2}}/r\]

Correct Answer: D

Solution :

[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. \[N\sin \theta =\frac{m{{v}^{2}}}{r}\Rightarrow N=\frac{1}{\sin \theta }\left( \frac{m{{v}^{2}}}{r} \right)\] and \[n\cos \theta =mg\Rightarrow N=\frac{mg}{\cos \theta }\] \[\because \sin \theta \]and \[\cos \theta <1\] So \[N>mg\] and \[N>\frac{m{{v}^{2}}}{r}\]