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 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

A particle of mass 200 g is moving in a circle of radius 2 m. The particle is just 'looping the loop'. The speed of the particle and the tension in the string at highest point of the circular path are (g=10 ms^-2)

1. 4 ms^-1, 5 N

2. 4.47 ms^-1, zero

3. 2.47 ms^-1, zero

4. 1 ms^-1, zero

A particle of mass 200 g, is whirled into a vertical circle of radius 80 cm using a massless string. The speed of the particle when the string makes an angle of $60°$ with the vertical line is 1.5 ms^-1. The tension in the string at this position is

1. 1 N

2. 1.56 N

3. 2 N

4. 3 N

A string tied on a roof bears a maximum tension of \(50\) kg-wt. The minimum acceleration that can be acquired by a man of \(98\) kg to descend will be:
[Take \(g=9.8\) m/s²]
1. \(9.8\) m/s²
2. \(4.9\) m/s²
3. \(4.8\) m/s²
4. \(5\) m/s²

A balloon has 2 g of air. A small hole is pierced into it. The air comes out with a velocity of 4 m/s. If the balloon shrinks completely in 2.5 s, the average force acting on the balloon is:

1. 0.008 N

2. 0.0032 N

3. 8 N

4. 3.2 N

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

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?
        

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?