Six particles situated at the corners of a regular hexagon of side \(a\) move at constant speed \(v\). Each particle maintains a direction towards the particle at the next. The time which the particles will take to meet each other is:
1. \(\frac{2 a}{v}~\text{sec}\)
2. \(\frac{a}{v}~\text{sec}\)
3. \(\frac{2 a}{3v}~\text{sec}\)
4. \(\frac{3 a}{v}~\text{sec}\)

In a uniform circular motion, which of the following quantity is not constant

1. Angular momentum

2. Speed

3. Kinetic energy

4. Momentum

A river is flowing with a speed of 1 km/hr. A swimmer wants to go to point 'C' starting from 'A'. He swims with a speed of 5 km/hr, at an angle $\theta$ with respect to the river. If \(\text {AB = BC = 400 m}\). Then

1. The time taken by the man is 12 min

2. The time taken by the man is 8 min

3. The value of $\theta$ is 45$°$

4. The value of $\theta$ is 53$°$

A particle starts from the origin at t=0 and moves in the x-y plane with constant acceleration 'a' in the y direction. Its equation of motion is $y=b{x}^2$. The x component of its velocity (at t=0) is:

1. variable

2. $\sqrt{\frac{2a}{b}}$

3. $\frac{a}{2b}$

4. $\sqrt{\frac{a}{2b}}$

A particle has initial velocity $\left(3\hat{\mathrm{i}}+4\hat{\mathrm{j}}\right)$ and has acceleration $\left(0.4\hat{\mathrm{i}}+0.3\hat{\mathrm{j}}\right)$. Its speed after 10 s:

1. 7 units

2. $7\sqrt{2}$ units

3. 8.5 units

4. 10 units

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

1. 10 km/hr

2. 8 km/hr

3. 6 km/hr

4. 4 km/hr

A train is moving towards east and a car is along north, both with same speed. The observed direction of car to the passenger in the train is 

1. East-north direction

2. West-north direction

3. South-east direction

4. None of these

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: