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 of \(10\) m/min. In which direction should the man swim so as to take the shortest possible path to go to the south:

1.	\(30^{\circ}\) with downstream
2.	\(60^{\circ}\) with downstream
3.	\(120^{\circ}\) 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 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 fly wheel making \(120\) revolutions/minute is:
1. \(2\pi~\mathrm{rad/s}\)
2. \(4\pi^2~\mathrm{rad/s}\)
3. \(\pi~\mathrm{rad/s}\)
4. \(4\pi~\mathrm{rad/s}\)

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

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

(1) 1600 m/sec²

(2) 4740 m/sec²

(3) 2370 m/sec²

(4) 5055 m/sec²

If a_r and a_t represent radial and tangential accelerations, the motion of a particle will be uniformly circular if 

1. a_r = 0 and a_t = 0

2. a_r = 0 but $a_t\ne 0$

3. $a_r\ne 0$ but a_t = 0

4. $a_r\ne 0$ and $a_t\ne 0$

In \(1.0~\text{s}\), a particle goes from point \(A\) to point \(B\), moving in a semicircle of radius \(1.0~\text{m}\) (see figure). The magnitude of the average velocity is:

The coordinates of a moving particle at any time \(t\) are given by \(x=\alpha t^3\) and \(y=\beta t^3.\) The speed of the particle at time \(t\) is given by:
1. \(\sqrt{\alpha^2+\beta^2}~\)
2. \(3t\sqrt{\alpha^2+\beta^2}~\)
3. \(3t^2\sqrt{\alpha^2+\beta^2}~\)
4. \(t^2\sqrt{\alpha^2+\beta^2}~\)