﻿ 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? from Physics Laws of Motion Class 11 Manipur Board

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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?

We have,

Mass of the stone, m = 0.25 kg

Radius of the circle, r = 1.5 m

Number of revolution per second, n =

40 / 60 = 2 / 3 rps
Angular velocity, ω =  = 2πn

The tension in the string provides the centripetal force.

i.e.,

T = Fcentripetal

=

= mrω

= mr(2πn)

= 0.25 × 1.5 × (2 × 3.14 × ()2
= 6.57 N

Maximum tension in the string,

Tmax = 200 N

max = mv2max / r

∴       vmax = (Tmax × r  / m)1/2

= (200 × 1.5 / 0.25)1/2

= (1200)1/2

= 34.64 m/s

Therefore, the maximum speed of the stone is 34.64 m/s.
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