A boy ties a stone of mass 100 g to the end of a 2 m long string and whirls it around in a horizontal plane. The string can withstand the maximum tension of 80 N. If the maximum speed with which the stone can revolve is K/π rev./min. The value of K is (Assume the string is massless and unstretchabl…

Question

A boy ties a stone of mass 100 g to the end of a 2 m long string and whirls it around in a horizontal plane. The string can withstand the maximum tension of 80 N. If the maximum speed with which the stone can revolve is K/π rev./min. The value of K is (Assume the string is massless and unstretchable)

Accepted Answer

(3) 600. Idea: get ω from the tension, then convert radians per second into revolutions per minute — the conversion is the whole question. T=mω²r: 80=0.1×ω²×2=0.2 ω² ω²=400, so ω=20 rad/s. In revolutions per minute, n=ω/(2π)×60=(20×60)/(2π)=(600)/π rev/min. Comparing with K/π gives K=600. Leaving the answer as (600)/π rather than 191 rpm is the examiner's way of checking that the factor (60)/(2π) was applied and not (60)/π.

Step-by-step solution

Why the other options are wrong