A boat is sent across a river in a perpendicular direction with a velocity of \(8\ \text{km/hr}\). If the resultant velocity of the boat is \(10\ \text{km/hr}\), then the velocity of the river is: 

1. \(10\ \text{km/hr}\)

2. \(8\ \text{km/hr}\) 

3. \(6\ \text{km/hr}\) 

4. \(4\ \text{km/hr}\) 

A train is moving towards the east and a car is along the north at the same speed. The observed direction of the car to the passenger on the train is:

If the body is moving in a circle of radius r with a constant speed v, its angular velocity is:

1. v²/r

2. vr

3. v/r

4. r/v

A motorcyclist going round in a circular track at a constant speed has:

1. constant linear velocity.

2. constant acceleration.

3. constant angular velocity.

4. constant force.

A particle moves with constant angular velocity in a circle. During the motion its:

The angular speed of a flywheel making \(120\ \text{revolutions/minute }\)is: 

1. \(2 𝜋\ \text{𝑟𝑎𝑑/𝑠}\) $\mathrm{}$

2. \(4 𝜋^2\ \text{𝑟𝑎𝑑/𝑠}\)$\mathrm{}$

3. \(𝜋\ \text{𝑟𝑎𝑑/𝑠}\)$$

4. \(4 𝜋\ \text{𝑟𝑎𝑑/𝑠}\)$\mathrm{}$

The angle turned by a body undergoing circular motion depends on time as \(\theta=\theta_0+\theta_1t+\theta_2t^2.\) Then the angular acceleration of the body is:
1. \(\theta_1\)

2. \(\theta_2\)

3. \(2\theta_1\)

4. \(2\theta_2\)

A bomb is dropped from an aeroplane moving horizontally at constant speed. When air resistance is taken into consideration, the bomb:

1. Falls to earth exactly below the aeroplane

2. Fall to earth behind the aeroplane

3. Falls to earth ahead of the aeroplane

4. Flies with the aeroplane

If a body \(A\) of mass \(M\) is thrown with a velocity \(v\) at an angle of \(30^°\) to the horizontal and another body \(B\) of the same mass is thrown with the same speed at an angle of \(60^°\) to the horizontal. The ratio of the horizontal range of \(A\) to \(B\) will be:

1. \(1 : 3\)

2. \(1 : 1\)

3. \(1 : \sqrt3\)

4. \( \sqrt3:1\)