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 Kg is whirled in a horizontal circle of radius 1 m by means of a string at an initial speed of 10 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