A cyclist riding a bicycle at a speed of \(14\sqrt3\ \text{ms}^{–1}\) takes a turn around a circular road of radius \( 20\sqrt3\ \text{m}\) without skidding. His inclination to the vertical is:

1. \(30^\circ\)

2. \(​​90^\circ\)

3. \(45^\circ\)

4. \(60^\circ\)

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. \(0.71\)

A motorcycle driver doubles his velocity when he is taking a turn. The force exerted outwardly will be:

1. Double
2. Half
3. \(4\) times
4. \( \frac 14\)

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 \(1\ \text{kg}\) stone at the end of \(1\ \text{m}\) long string is whirled in a vertical circle at a constant speed of \(4\ \text{m/s}\). The tension in the string is \(6\ \text{N}\), when the stone is at: (Take \(g = 10\ \text{m/s}^2\)) 

1. Top of the circle
2. Bottom of the circle
3. Half way down
4. None of the above