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InterviewSolution
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A particle of mass 100 g, is made to describe a vertical circle of radius 1 m. Its instantaneous speed is `1ms^(-1)` when the string makes an sngle of `30^(@)` with the vertical Find the tension in the string at this position. Can the particle complete its circular path? `(g=10ms^(-2))` |
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Answer» Tension in the string when it make an angle `theta` with the vertical is `T=(mv^(2))/®+mg cos theta` Let speed at the lowest point be `v_(1)` `v_(1)^(2)=v^(2)+2gr(1-costheta)` `(v_(1))_(min)=sqrt(5gr)"chect if"v_(1)lt(v_(1))_(min).` If yes, then it would not complete its vertical circular path. The tension in the string. when it makes and angle `theta` with the vertical is `T=(mv^(2))/(r)+mgcostheta` `=(0.1xx1^(2))/(1)+0.1xx10xx0.866=0.966N` let the speed at the lowest point be `v_(1)` `v_(1)^(2)=v^(2).+2gr(1-costheta)` `=1^(2)+2xx10xx1xx(1-0.866)` `=1+20xx0.134` `=3.68` `v_(1)=sqrt3.68=1.91ms^(-1)` `(v_(1))_(min)=sqrt(5gr)=sqrt(5xx10xx1)=7.07ms^(-1)` `v_(1)lt(v_(1))_(min)implies` the particle would not be able to complete its circular path. |
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