What determines the nature of the path followed by the particle?

1. Speed only

2. Velocity only

3. Acceleration only

4. None of these

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 boat moves with a speed of \(5\ \text{km/h}\) relative to water in a river flowing with a speed of \(3\ \text{km/h}\) and having a width of \(1\ \text{km}\). The minimum time taken for a round trip (returning to the initial point) is:

1. \(5\ \text{min}\)

2. \(60\ \text{min}\)

3. \(20\ \text{min}\)

4. \(30\ \text{min}\)

A river is flowing from W to E with a speed of 5 m/min. A man can swim in still water with a velocity 10 m/min. In which direction should the man swim so as to take the shortest possible path to go to the south. 

1. 30° with downstream

2. 60° with downstream

3. 120° with downstream

4. South

If a particle moves in a circle describing equal angles in equal times, its velocity vector:

1. remains constant.

2. changes in magnitude.

3. changes in direction.

4. changes both in magnitude and direction.

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 \(P\) is moving in a circle of radius \(a\) with a uniform speed \(v\). \(C\) is the centre of the circle and \(AB\) is a diameter. When passing through \(B\) the angular velocity of \(P\) about \(A\) and \(C\) are in the ratio:

1. \(1 : 1\)

2. \( 1 : 2\)

3. \(2 : 1\)

4. \(4 : 1\)

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. \(4 𝜋\ \text{𝑟𝑎𝑑/𝑠}\)$\mathrm{}$

Certain neutron stars are believed to be rotating at about \(1\ \text{rev/sec}\). If such a star has a radius of \(20\ \text{km}\), the acceleration of an object on the equator of the star will be:

1. \(20×10^8\ \text{m/s}^2\)

2. \(8×10^5\ \text{m/s}^2\)

3. \(120×10^5\ \text{m/s}^2\) $\mathrm{}$

4. \(4×10^8\ \text{m/s}^2\)$\mathrm{}$

An electric fan has blades of length \(30\ \text{cm}\) as measured from the axis of rotation. If the fan is rotating at \(1200\ \text{r.p.m}\), the acceleration of a point on the tip of the blade is about:

1. \(1600\ \text{m/s}^2\)

2.  \(4740\ \text{m/s}^2\)

3. \(2370\ \text{m/s}^2\)

4. \(5055\ \text{m/s}^2\)