Banking of Roads

Q. A curved road of radius $50m$ is banked at correct angle for a given speed. If the speed is to be doubled keeping the same banking angle, the radius of curvature of the road should be changed to

1. $25\text{m}$
2. $100\text{m}$
3. $150\text{m}$
4. $200\text{m}$

Q. A circular race-car track of radius $300\text{m}$ is banked at an angle of ${15}^{\circ }$. If the coefficient of static friction between the wheels of the race-car and the road is $0.2$, what is the maximum permissible speed to avoid slipping? Take $\tan {15}^{\circ }=0.27,g=10{\text{m/s}}^2$.

1. $48\text{m/s}$
2. $30\text{m/s}$
3. $17\text{m/s}$
4. $38.60\text{m/s}$

Q. A string attached to a light thread is whirled in a vertical circle with a constant velocity $v$. The radius of the circle is $10\text{m}$. The maximum and minimum tension of the string is in the ratio $4:1$. What is the value of velocity $v$?
(Take $g=10{\text{m/s}}^2$)

1. $15.1\text{m/s}$
2. $13.5\text{m/s}$
3. $12.9\text{m/s}$
4. $10.9\text{m/s}$