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:

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: