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

Question

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

Infinity Learn · Accepted Answer

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 $$2$$ $$kx$$$$=ml$$ω$$2+mx$$ω$$2x(k$$−mω$$2)=ml$$ω$$2$$ $$x=ml$$ω$$2k$$−mω$$2$$

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