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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The correct Answer is:

(A)P,S; (B)P,Q,S; (C )P,R; (D)P

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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.

for `0 lt v lt sqrt((GM)/r` trajectory may be ellipse

for v `=sqrt((GM)/r` trajectory may be ellipse

for `sqrt((GM)/r lt v lt sqrt((2GM)/r` trajectory may be ellipse.

for v `=sqrt((GM)/r trajectory may be circle

`(A rarr s, B rarr r,C rarrp, D rarr q)`

`(A rarr c, B rarr s,C rarrp, D rarr q)`

`(A rarr s, B rarr r,C rarrq, D rarr p)`

`(A rarr q, B rarr r,C rarrp, D rarr s)`

(i)-(d), (ii)-(b), (iii)-(c ), (iv)-(a)

(i)-(a), (ii)-(b), (iii)-(c ), (iv)-(d)

(i)-(b), (ii)-(c ), (iii)-(d), (iv)-(a)

(i)-(d), (ii)-(b), (iii)-(a), (iv)-(c )