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a particle is attached to the end of the vertical rod with the other end hinged.the particle is now imparted velocity such that it completes vertical revolution.the rod is inclined at the angle sin^-(1/x) with the horizantal when the net force on the particle is horizantal.what is value of x

a particle is attached to the end of the vertical rod with the other end hinged.the particle is now imparted velocity such that it completes vertical revolution.the rod is inclined at the angle sin^-(1/x) with the horizantal when the net force on the particle is horizantal.what is value of x

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1 Answers

Chetan Mandayam Nayakar
312 Points
11 years ago

let l be the length of the rod. At the top of the circle, velocity =zero. thus when angle =arcsin(x), KE =mgl(1+x)=(mv^2)/2

v^2=2gl(1+x). NET FORCE ON PARTICLE IS ZERO WHEN VERTICAL COMPONENT OF CENTRIPETAL FORCE BALANCES GRAVITY.

v2/l =2g(1+x),v2x/l=2gx(1+x), Now we thus have 2gx(1+x)=g, x=(√3-1)/2

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