Two particles of equal mass are revolving in circular paths of radii \(r_1\) and \(r_2\) respectively, with the same speed. The ratio of their centripetal forces is:

1. \(\dfrac{r_2}{r_1}\)

2. \(\sqrt{\dfrac{r_2}{r_1}}\)

3. \(\dfrac{r_1^2}{r_2}\)

4. \(\dfrac{r_2^2}{r_1}\)

If the overbridge is concave instead of being convex, the thrust on the road at the lowest position will be:
1. \(mg+\dfrac{mv^2}{r}\)
2. \(mg-\dfrac{mv^2}{r}\)
3. \(\dfrac{mv^2g}{r}\)
4. \(\dfrac{v^2g}{r}\)

A particle moves in a circular orbit under the action of a central attractive force inversely proportional to the distance \(r\). The speed of the particle is:

1. Proportional to \(r^2\)

2. Independent of \(r\)

3. Proportional to \(r\)

4. Proportional to \(\dfrac 1r\)

A \(500\ \text{kg}\) car takes a round turn of radius \(50\ \text{m}\) with a velocity of \(36\ \text{km/h}\). The centripetal force is:

1. \(250\ \text{N}\)

2. \(750\ \text{N}\)

3. \(1000\ \text{N}\)

4. \(1200\ \text{N}\)

A stone of mass \(16\ \text{kg}\) is attached to a string \(144\ \text{m}\) long and is whirled in a horizontal circle. The maximum tension the string can withstand is \(16\ \text{N}\). The maximum velocity of revolution that can be given to the stone without breaking it will be:

1. \(20\ \text{ms}^{–1}\)
2. \(16\ \text{ms}^{–1}\)
3. \(14\ \text{ms}^{–1}\)
4. \(12\ \text{ms}^{–1}\)

A point mass \(m\) is suspended from a light thread of length \(l,\) fixed at \(O\), and is whirled in a horizontal circle at a constant speed as shown. From your point of view, stationary with respect to the mass, the forces on the mass are:

1.		2.
3.		4.

If a cyclist moving at a speed of \(4.9\ \text{m/s}\) on a level road can take a sharp circular turn of radius \(4\ \text{m}\), then the coefficient of friction between the cycle tyres and the road is:

1. \( 0.41\)
2. \(0.51\)
3.\( 0.61\)
4. \(0.71\)

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 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. \(1\ \text{cm}\)