Question

A road is banked such that a vehicle can go in the middle of it with a constant velocity of 40 m/s. What will happen if the velocity is decreased and why?
Imagine friction is not present

• A. The vehicle will slide down as Normal by ground will decrease.
• B. The vehicle slide up as Normal by ground will increase
• C. The vehicle will slide down as centripetal force mv²/R has to be constant
• D. None of these

Answer 1

The correct option is C

The vehicle will slide down as centripetal force mv²/R has to be constant

N cos $\theta$ = mg ............ (i)

N sin $\theta$ = m $\frac{v^2}{R}$ ........... (ii)

Mg is constant as neither mass nor acceleration due to gravity can change.

So in equation (i) this means N cos $\theta$ = constant

Also $\theta$ is fixed i.e. the banking of road to cos $\theta$ is fixed

$\Rightarrow$ N is constant
$\Rightarrow$ in equation (ii) N sin = constant so $\frac{m{v}^2}{R}$ should be constant
2 Now question is saying to decrease velocity since if v decreases $\frac{m{v}^2}{R}$ will decrease but as it has to remain
mv2 constant so the R will change in such a way to keep $\frac{m{v}^2}{R}$ as constant. So R will decrease.

So block will slide down.

Well I guess you know all this intuitively