A stone of mass 0.25 kg tied to the end of a string is whirled round in a circle of radius 1.5 m with a speed of 40 rev./min in a horizontal plane. What is the tension in the string? What is the maximum speed with which the stone can be whirled around if the string can withstand a maximum tension of 200 N?
The angular velocity of the stone in circular motion is given as,
ω = 
where,
‘v’ is the linear velocity
‘r’ is the radius of the circle.
‘n’ is the number of revolutions per second
The centripetal force for the stone is provided by the tension T of the string,
The centripetal force ‘Fc’ can be given as
Fc 
ω2r = m (2πn)2 r
And Fc = Tension in the string
Where, m
Given,
Mass of the stone, m= 0.25 kg
Radius of the circle, r= 1.5 m
Number of the revolution per second, n = 
⇒ n= 
Thus,
T= Fc = 
⇒ T = 6.57 N
The tension in the string is 6.57 N
Given,
The maximum tension that the string can withstand is, T’ =200 N
T’= 
⇒ v’= 
Where, v’ is the maximum velocity of the stone
⇒ v’ =
The maximum speed of the stone is 34.64 m/s