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

In a cricket match, the fielder draws his hands backward after receiving the ball in order to take a catch because:

1. His hands will be saved from getting hurt.

2. He deceives the player.

3. It is a fashion.

4. He catches the ball firmly.

A body is placed on a rough inclined plane of inclination $\mathrm{\theta }$. As the angle $\mathrm{\theta }$ is increased from 0^o to 90^o , the contact force between the block and the plane

1. Remains constant

2. First remains constant then decreases

3. First decreases then increases

4. First increases then decreases

A particle of mass \(200\text{ g}\) is moving in a circle of radius \(2\text{ m}.\) 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 (\(g=10\text{ m/s}^2\))

1. \(4 \text{ m/s}, ~5\text{ N}\)

2. \(4.47 \text{ m/s}, ~\text{zero}\)

3. \(2.47 \text{ m/s}, ~\text{zero}\)

4. \(1 \text{ m/s}, ~\text{zero}\)

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 $4<mspace\; width="1em"></mspace>{\mathrm{ms}}^{-1}$ 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 bullet of mass 0.012 kg and horizontal speed $70<mspace\; width="1em"></mspace>m<mspace\; width="1em"></mspace>s^{-1}$ 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 \(300\) 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?

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