Banking Of Road - Practice Questions & MCQ

A train is moving with a speed of $12\mathrm{m}/\mathrm{s}$ on rails which are $1.5\mathrm{m}$ apart. To negotiate a curve of radius $400\mathrm{m}$, the height by which the outer rail should be raised with respect to the inner rail is (Given, $g=10\mathrm{m}/{\mathrm{s}}^2$ )

A car of $800\mathrm{kg}$ is taking turn on a banked road of radius $300\mathrm{m}$ and angle of banking ${30}^{\circ }$. If the coefficient of static friction is 0.2 then the maximum speed with which the car can negotiate the turn safely: $(\mathrm{g}=10\mathrm{m}/{\mathrm{s}}^2,\sqrt{3}=1.73)$

A car of mass m is moving on a concave bridge of radius r with velocity v as shown in the diagram for what value of the reaction on the car by the bridge will be maximum. 

Where $\theta$ is the angle made by a vertical line