If a cyclist moving with a speed of 4.9 m/s on a level road can take a sharp circular turn of radius 4 m, then coefficient of friction between the cycle tyres and road is 

1. 0.41

2. 0.51

3. 0.61

4. 0.71

A motor cycle driver doubles its velocity when he is having a turn. The force exerted outwardly will be

1. Double

2. Half

3. 4 times

4. $\frac{1}{4}$ times

Two bodies of equal masses revolve in circular orbits of radii R₁ and R₂ with the same period. Their centripetal forces are in the ratio

(1) ${\left(\frac{{\displaystyle R_2}}{{\displaystyle R_1}}\right)}^2$

(2) $\frac{R_1}{R_2}$

(3) ${\left(\frac{{\displaystyle R_1}}{{\displaystyle R_2}}\right)}^2$

(4) $\sqrt{R_1{R}_2}$

A mass is supported on a frictionless horizontal surface. It is attached to a string and rotates about a fixed centre at an angular velocity ω₀. If the length of the string and angular velocity are doubled, the tension in the string which was initially T₀ is now 

1. T₀

2. T₀/2

3. 4 T₀

4. 8 T₀

Three identical particles are joined together by a thread as shown in figure. All the three particles are moving in horizontal circles centred at O. If the velocity of the outermost particle is v₀, 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