An aircraft executes a horizontal loop at a speed of \(720\) km/h with its wings banked at \(15^{\circ}\). What is the radius of the loop? (Take \(g=10~\text{m/s}^{2}\), \(\tan 15^{\circ}=0.27\))$$
1. \(1.30\) km
2. \(14.9\) km
3. \(1.55\) km
4. \(20.9\) km

A train runs along an unbanked circular track of radius \(30\) m at a speed of \(54\) km/h. The mass of the train is \(10^{6}\) kg. What is the angle of banking required to prevent wearing out of the rail?
1. \(30^\circ\)
2. \(45^\circ\)
3. \(53^\circ\)
4. \(37^\circ\)