Question

A body of mass 2kg is tied to one end of the string of length 1 m and is whirled in a horizontal circle with 15rpm. find the tension in the string

Answer 1

t=mr(w)2
=2×1×15×15
=450N

Answer 2

$\sf \:Given :\\\\m=2\:kg\\R= 1\:m\\f_{max}=15 \:rpm= \frac{15}{60} \:rps=\frac{1}{4}\:rps$

$\sf v_{max}=R×w_{max}\\\\v_{max}=R(2πf_{max})\\\\v_max=1×2×22/7×\frac{1}{4}\\\\\underline{\underline{v_{max}=\frac{11}{7} m/s}}$

$\sf \:Maximum\:Tension\:force\:in\:string\\T_{max}=\frac{m{v_{max}}^{2}}{R}\\\\\therefore\:T_{max}=\frac{2×{\frac{11}{7}}^{2}}{1}\\\\T_{max}=\frac{242}{7}=34.57\:N$

$\underline{\boxed{\sf{Tension\:on\:the\:string\:is\:34.6\:N}}}$