A stone of mass of 16 kg is attached to a string 144 m long and is whirled in a horizontal circle. The maximum tension the string can withstand is 16 Newton. The maximum velocity of revolution that can be given to the stone without breaking it will be-

1. 20 ms^–1

2. 16 ms^–1

3. 14 ms^–1

4. 12 ms^–1

Find the maximum velocity for skidding for a car moved on a circular track of radius 100 m. The coefficient of friction between the road and tyre is 0.2 

1. 0.14 m/s

2. 140 m/s

3. 1.4 km/s

4. 14 m/s

A ball of mass \(0.1~\text{kg}\) is whirled in a horizontal circle of radius \(1\) m by means of a string at an initial speed of \(10~\text{rpm}\) . Keeping the radius constant, the tension in the string is reduced to one quarter of its initial value. The new speed is:

A cyclist riding the bicycle at a speed of $14\sqrt{3}$ms^–1 takes a turn around a circular road of radius $20\sqrt{3}$m without skidding. Given g = 9.8 ms^–2, what is his inclination to the vertical?

1. 30^o

2. 90^o

3. 45^o

4. 60^o

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 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