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 \(120\ \text{revolutions/minute }\)is: 

1. \(2 𝜋\ \text{𝑟𝑎𝑑/𝑠}\) $\mathrm{}$

2. \(4 𝜋^2\ \text{𝑟𝑎𝑑/𝑠}\)$\mathrm{}$

3. \(𝜋\ \text{𝑟𝑎𝑑/𝑠}\)$$

4. \(4 𝜋\ \text{𝑟𝑎𝑑/𝑠}\)$\mathrm{}$

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

1. \(20×10^8\ \text{m/s}^2\)

2. \(8×10^5\ \text{m/s}^2\)

3. \(120×10^5\ \text{m/s}^2\) $\mathrm{}$

4. \(4×10^8\ \text{m/s}^2\)$\mathrm{}$

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

1. \(1600\ \text{m/s}^2\)

2.  \(4740\ \text{m/s}^2\)

3. \(2370\ \text{m/s}^2\)

4. \(5055\ \text{m/s}^2\)

The angular speed of the second hand in a mechanical watch is:

1. \(\dfrac{\pi}{30}\ \text{rad/s}\) 

2. \(2\pi\ \text{rad/s}\)

3. \(\pi\ \text{rad/s}\)

4. \(\dfrac{60}{\pi}\ \text{rad/s}\)

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. \(2\pi v^2 / T\)

          
1. \(3.14~\text{m/s}\)
2. \(2.0~\text{m/s}\)
3. \(1.0~\text{m/s}\)
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?