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+1 vote
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in Physics by (54.6k points)

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?

1 Answer

+1 vote
by (54.6k points)
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Best answer

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 = / = 2 ………………….(i)

The centripetal force for the stone is provided by the tension T, in the string, i.e.,

T = FCentripetal 

= mv2/r = mrω2 = mr(2πn)2 

= 6.57 N

Maximum tension in the string, Tmax = 200 N

Tmax = mv2max /r

vmax = √Tmax x r/m

√200 x 1.5/0.25

√1200 = 34.64 m/s

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

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