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 ?

Explanation

Here , m =0.25 kg , r = 1.5 m ,
`n=40" rpm"=(40)/(60)" rps"=(2)/(3)" rps",T=`?
`T=m" r "omega^(2)=m " r" (2pi" n")^(2)=4pi^(2)m" r "n^(2)`
`T=4xx(22)/(7)xx(22)/(7)xx0.25xx1.5xx((2)/(3))^(2)=6.6N`
If `T_("max")=200N," then from " T_("max")=(mv_("max")^(2))/(r)`
`rArr v_("max")^(2)=(T_("max")xxr)/(m)=(200xx1.5)/(0.25)=1200`
`v_("max")=sqrt(1200)=34.6m//s`