V=sqrt((GM)/(r))

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

Check the dimensional consistency of the following equations : (i) de-Broglie wavelength , lambda=(h)/(mv) (ii) Escape velocity , v=sqrt((2GM)/(R)) .

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"):}

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"):}

Statement-1 : Two satellites of mass 3 M and M orbit the earth in circular orbits of radii r and 3r respectively. The ratio of their speeds is sqrt(3) : 1 . Statement-2 : Orbital velocity of satellite is upsilon = sqrt((GM)/(r ))

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

Check the dimensional consistency of the following equations. (ii) Escape velocity, v=sqrt((2GM)/(R ))

Check the correctness of the physical relation: v= sqrt((2GM)/(R)) , where v is velocity, G is gavitational constant, M is mass and R is radius of the earth.

Escape velocity: V_(esc) = sqrt((2GM)/(R)) for earth : V_(esc) = 11.2 km//s If mass of a planet is eight times the mass of the earth and its radius is twice the radius of the earth , what will be the escape velocity for that planet ?