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

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

Two bodies of mass 10 kg and 5 kg moving in concentric orbits of radii R and r such that their periods are the same. Then the ratio between their centripetal acceleration is 

(1) R/r

(2) r/R

(3) R²/r²

(4) r²/R²

A particle is moving in a horizontal circle with constant speed. It has constant 

(1) Velocity

(2) Acceleration

(3) Kinetic energy

(4) Displacement

The angular speed of a flywheel making 120 revolutions/minute is: 

(1) $2\pi rad/s$

(2) $4{\pi }^{2}rad/s$

(3) $\pi rad/s$

(4) $4\pi rad/s$

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

(1) $20\times {10}^{8}m/{\sec }^2$

(2) $8\times {10}^{5}m/{\sec }^2$

(3) $120\times {10}^{5}m/{\sec }^2$

(4) $4\times {10}^{8}m/{\sec }^2$

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

The angular speed of seconds needle in a mechanical watch is:

(1) $\frac{\pi }{30}$ rad/s

(2) 2π rad/s

(3) π rad/s

(4) $\frac{60}{\pi }$ rad/s

What is the value of linear velocity if \(\overset{\rightarrow}{\omega} = 3\hat{i} - 4\hat{j} + \hat{k}\) and \(\overset{\rightarrow}{r} = 5\hat{i} - 6\hat{j} + 6\hat{k}\)  :

A particle moves with constant speed v along a circular path of radius r and completes the circle in time T. The acceleration of the particle is:

1. $2$ $\pi$ $v/T$

2. $2$ $\pi$ $r/T$

3. $2$ $\pi$ $r^2/T$

4. $2$ $\pi$ $v^2/T$