(A)→(P), (Q)
Quantity given in option (A) has a dimension of force ×
(length)2 ; quantities given in options (P) and (Q) has the same dimensions:
GMeMs =
Fr2 or its unit is
kgm3s−2.
(B)→(R), (S)
We have
=
Cmax2 ⇒ the unit
m2s−2, which is nothing but energy per unit mass; the dimensions of this quantity is
L∕T2;
quantities given in options (R) and (S) have the same dimension.
(C)→(R), (S)
We have
=
v2 ⇒ the unit
m2s−2, that is, the condition is
same as that of option (B).
(D)→(R), (S)
It is square of the escape velocity of the Earth:
=
Vg =
⇒ the unit ;
m2s−2 The dimensions are same as that of option (B).