(A)→(P), (Q)
Quantity given in option (A) has a dimension of force ×
length2 ; quantities given in options (P) and (Q) has the same dimensions:
GMe​Ms​ =
Fr2 or its unit is
kgm3s−2.
(B)→(R), (S)
We have
M3RT​ =
Cmax2​ ⇒ the unit
m2s−2, which is nothing but energy per unit mass; the dimensions of this quantity is
T2L​;
quantities given in options (R) and (S) have the same dimension.
(C)→(R), (S)
We have
q2B2F2​ =
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:
ReGMe​ =
Vg​ =
W/m ⇒ the unit ;
m2s−2 The dimensions are same as that of option (B).