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Match the column : A particle at a dis...

Match the column :
A particle at a distance r from the centre of a uniform spherical planet of mass M radius `R(lt r)` has a velocity v magnitude of which is given in column I. Match trajectory from column II about possible nature of orbit.
`{:(,"Column I",,"Column II"),((A),0lt V lt sqrt((GM)/(r )),(P),"Straight line"),((B),sqrt((GM)/(r )),(Q),"Circle"),((C ),sqrt((2GM)/(r )),(R ),"Parabola"),((D),v gt sqrt((2GM)/(r )),(S ),"Ellipse"):}`

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A particle at a distance r from the centre of a uniform spherical planet of mass M radius R (ltr) has a velocity of magnitude v.

v_(e)=sqrt((2GM)/(R))

Match the following columns. (for a satellite in circular orbit) {:(,"Column-I",,"Column-II"),("(A)","Kinetic energy","(p)",-(GMm)/(2r)),("(B)","Potential energy","(q)",sqrt((GM)/(r))),("(C)","Total energy","(r)",-(GMm)/(r)),("(D)","Orbital speed","(s)",(GMm)/(2r)):}

Match the following columns. (for a satellite in circular orbit) {:(,"Column-I",,"Column-II"),("(A)","Kinetic energy","(p)",-(GMm)/(2r)),("(B)","Potential energy","(q)",sqrt((GM)/(r))),("(C)","Total energy","(r)",-(GMm)/(r)),("(D)","Orbital speed","(s)",(GMm)/(2r)):}

{:(,"Column I",,"Column II"),(("A"),R//L,(p),"Time"),(("B"),C//R,(q),"Frequency"),(("C"),E//B,(r),"Speed"),(("D"),sqrt(epsilon_(0)mu_(0)),(s),"None"):}

{:(,"Column I",,"Column II"),(("A"),R//L,(p),"Time"),(("B"),C//R,(q),"Frequency"),(("C"),E//B,(r),"Speed"),(("D"),sqrt(epsilon_(0)mu_(0)),(s),"None"):}

Given that v=sqrt((2GM)/(R )) . Find log v.