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. \(37^\circ\)

A monkey of mass \(40\) kg climbs on a massless rope (as shown in the figure) which can stand a maximum tension of \(600\) N. In which of the following cases will the rope break?
        

The rear side of a truck is open and a box of 40 kg mass is placed 5 m away from the open end as shown in Figure. The coefficient of friction between the box and the surface below it is 0.15. On a straight road, the truck starts from rest and accelerates with $2 m s^{-2}$. At what distance from the starting point does the box fall off the truck? (Ignore the size of the box).

1. 15.5 m
2. 40.5 m
3. 18.8 m
4. 25.0 m

What is the minimum speed required at the uppermost position to perform a vertical loop if the radius of the chamber is \(25\) m?
1. \(16.7\) m/s
2. \(15.8\) m/s
3. \(35\) m/s
4. \(24\) m/s

A 70 kg man stands in contact against the inner wall of a hollow cylindrical drum of radius 3 m rotating about its vertical axis with 200 revs/min. The coefficient of friction between the wall and his clothing is 0.15. What is the minimum rotational speed of the cylinder to enable the man to remain stuck to the wall (without falling) when the floor is suddenly removed?

1. 3.14 rad/s
2. 4.17 rad/s
3. 4.71 rad/s
4. 3.21 rad/s

A trolley of mass \(300\) kg carrying a sandbag of \(25\) kg is moving uniformly with a speed of \(27\) km/h on a frictionless track. After a while, the sand starts leaking out of a hole on the floor of the trolley at the rate of \(0.05\) kgs^-1. What is the speed of the trolley after the entire sandbag is empty?
1. \(27\) km/h
2. \(7.7\) km/h
3. \(20\) km/h
4. \(19.6\) km/h

A bullet of mass 0.012 kg and horizontal speed $70 m s^{-1}$ strikes a block of wood of mass 0.4 kg and instantly comes to rest with respect to the block. The block is suspended from the ceiling by means of thin wires. The height to which the block rises is:

1. 11.2 cm
2. 12.7 cm
3. 28.5 cm
4. 21.2 cm

A trolley of mass 200 kg moves with a uniform speed of 36 km/h on a frictionless track. A child of mass 20 kg runs on the trolley from one end to the other (10 m away) with a speed of $4 {\mathrm{ms}}^{-1}$ relative to the trolley in a direction opposite to its motion, and jumps out of the trolley. What is the final speed of the trolley?

1. 1.01 m/s
2. 10.36 m/s
3. 9.64 m/s
4. 11.20 m/s

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 stream of water flowing horizontally with a speed of \(15\) ms^-1 pushes out of a tube of cross-sectional area \(10^{-2}\) m² and hits a vertical wall nearby. What is the force exerted on the wall by the impact of water, assuming it does not rebound? (Density of water, \(\rho=10^{3}\)  kg-m^-3)
1. \(1500\) N
2. \(2250\) N
3. \(1650\) N
4. \(2200\) N