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) $4\pi rad/s$

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 \(\overrightarrow{\omega} = 3\hat{i} - 4\hat{j} + \hat{k}\) and \(\overrightarrow{r} = 5\hat{i} - 6\hat{j} + 6\hat{k}\):

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. \(2\pi v^2 / T\)

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 \(\neq\) 0
3. a_r \(\neq\) 0 but a_t = 0
4. a_r \(\neq\) 0 and a_t \(\neq\) 0$\mathrm{}$
 

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

   
1. \(3.14\) m/s
2. \(2.0\) m/s
3. \(1.0\) m/s
4. zero

A stone tied to the end of a string of \(1\) m long is whirled in a horizontal circle with a constant speed. If the stone makes \(22\) revolutions in \(44\) s, what is the magnitude and direction of acceleration of the stone?