Two bodies of equal mass revolve in circular orbits of radii \(R_1\) and \(R_2\) with the same period. Their centripetal forces are in the ratio:
1. \(\left(\dfrac{R_2}{R_1}\right)^2\)
2. \(\dfrac{R_1}{R_2}\)
3. \(\left(\dfrac{R_1}{R_2}\right)^2\)
4. \(\sqrt{R_1R_2}\)

Three identical particles are joined together by a thread as shown in the given figure. All three particles are moving in horizontal circles centred at \(O\). If the velocity of the outermost particle is \(v_0\), then the ratio of tensions in the three sections of the string is:

1. \(3 : 5 : 7\)
2. \(3 : 4 : 5\)
3. \(7 : 11 : 6\)
4. \(3 : 5 : 6\)

A block of mass \(m\) at the end of a string is whirled round in a vertical circle of radius \(R\). The critical speed of the block at the top of its swing below which the string would slacken before the block reaches the top is:

1. \(Rg\)
2. \((Rg)^2\)
3.  \(R/g\)
4. \(\sqrt{Rg}\)

A bucket tied at the end of a 1.6 m long string is whirled in a vertical circle with constant speed. What should be the minimum speed so that the water from the bucket does not spill, when the bucket is at the highest position (Take g = 10 m/s²) 

1. 4 m/sec

2. 6.25 m/sec

3. 16 m/sec

4. None of the above

A 1 kg stone at the end of 1 m long string is whirled in a vertical circle at constant speed of 4 m/sec. The tension in the string is 6 N, when the stone is at (g = 10 m/sec²) 

1. Top of the circle

2. Bottom of the circle

3. Half way down

4. None of the above

The tension in the string revolving in a vertical circle with a mass m at the end which is at the lowest position 

1. $\frac{m{v}^2}{r}$

2. $\frac{m{v}^2}{r}-mg$

3. $\frac{m{v}^2}{r}+mg$

4. mg

A coin, placed on a rotating turntable, slips when it is placed at a distance of \(9\ \text{cm}\) from the centre. If the angular velocity of the turntable is tripled, it will just slip if its distance from the centre is:

1. \(27\ \text{cm}\)
2. \(9\ \text{cm}\)
3. \(3\ \text{cm}\)
4. \(1\ \text{cm}\)

A body of mass \(0.4\ \text{kg}\) is whirled in a vertical circle, making \(2\ \text{rev/s}\). If the radius of the circle is \(2\ \text{m}\), then the tension in the string when the body is at the top of the circle is:

1. \(41.56\ \text{N}\)
2. \(89.86\ \text{N}\)
3. \(109.86\ \text{N}\)
4. \(122.4\ \text{N}\)

A bucket full of water is revolved in vertical circle of radius 2m. What should be the maximum time-period of revolution so that the water doesn't fall off the bucket ?

1. 1 sec

2. 2 sec

3. 3 sec

4. 4 sec