Question

Which of the following values best represents the maximum velocity that a car can travel across hill depicted above if $R$ has a value of $15m$?

• A. $6\frac{m}{s}$
• B. $12\frac{m}{s}$
• C. $17\frac{m}{s}$
• D. $24\frac{m}{s}$
• E. $28\frac{m}{s}$

Answer 1

The correct option is B $12\frac{m}{s}$

Given : $R=15$ m

Let the maximum speed of the car be $v_{max}$.

Using circular motion we get $\frac{m{v}^2}{R}=mg-N$

For maximum speed, $N=0$

$\therefore$ $\frac{m{v}_{max}^2}{R}=mg$ $⟹v_{max}=\sqrt{gR}$

$\therefore$ Maximum speed of the car $v_{max}=\sqrt{9.8\times 15}\approx 12$ m/s