A particle of mass ‘m ’ is fixed to one end of light spring having force constant ‘k ’and unstretched length  ‘l ’. The other end is fixed. The system is given an angular speed ω  about the fixed end of the spring such that it rotates in a circle in gravity free space. Then the stretch in the spring is

restoring force of a spring is F=-kx, --=(1) here k is force constant, x is displacement centrifugal force acting on the mass attached to spring is F=m(l+x)w2 ,---(2)  here m is mass attached to the spring and l is unstretched length of spring equating above two equations 1 and 2 kx=mlω2+mxω2x(k−mω2)=mlω2 x=mlω2k−mω2