Question

Velocity of Parivle(v) depends on universal grivitional constant(G) radius(R) and Density(d) Then established the formula of velocity in terms of G,R,d.

Answer 1

[V]=[G]^a [R]^b [D]^c
[M^0 L^1 T^-1] =[M^0L^1T^-2]^a [M^0L^1T^0]^b [M^1L^-3T^0]^c
[M^0 L^1 T^-1] =[M^0aL^1aT^-2a] [M^0bL^1bT^0b][M^1cL^-3cT^0c]
[M^0 L^1 T^-1]=[M^0a+0b+c L^1a+1b-3c T^-2a+0b+0c]
0=0a+0b+c 1=1a+1b-3c. -1=-2a+0b+0c
0=c. 1=1a+1b a=1/2
1=1/2 +b
-1/2=b
[V]=[G]^a [R]^b [D]^c
[V]=[G]^1/2 [R]^-1/2 [D]^0