A circular freeway entrance and exit are commonly banked to control a moving car at $14 \mathrm{~m} / \mathrm{s}$. To design similar ramp for $28 \mathrm{~m} / \mathrm{s}$ one should

A cyclist leans with the horizontal at angle $30^{\circ}$, while negotiating round a circular road of radius $20 \sqrt{3} \mathrm{~m}$. The speed of the cycle should be

A point $P$ is moving in uniform circular motion with radius 3 m . Let at some instant the acceleration of the point is $\quad \mathbf{a}=(6 \hat{\mathbf{i}}-4 \hat{\mathbf{j}}) \mathrm{m} / \mathrm{s}^2$, the position vector is $\mathbf{r}$ and velocity vector is $\mathbf{v}$. Choose the correct statement.

If a body moving in a circular path maintains constant speed of $10 \mathrm{~ms}^{-1}$, then which of the following correctly describes the relation between acceleration (a) and radius $(r)$ ?