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 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 turn-table slips, when it is placed at a distance of 9 cm from the centre. If the angular velocity of the turn-table is trippled, it will just slip, if its distance from the centre is 

1. 27 cm

2. 9 cm

3. 3 cm

4. 1 cm

A body of mass 0.4 kg is whirled in a vertical circle making 2 rev/sec. If the radius of the circle is 2 m, then tension in the string when the body is at the top of the circle, is 

1. 41.56 N

2. 89.86 N

3. 109.86 N

4. 122.4 N