Question

Check tha dimensional consistency of tha equations

v=$\frac{\sqrt{GM} }{R}$
v=velocity
g=Gravitational constant
M=Mass
R=Radius

Answer 1

$\color{blue}{Answer}$

you mean, we have to check v=$\sqrt{\frac{2GM}{R}}$

is dimensionally correct or not . right ?

okay, first of all, we identify what is G , M, R and v .

G is gravitational constant.so, unit of G = Nm²/Kg²

and dimension of G = [M^-1L^3T^-2]

M is mass so, unit of M = kg

and dimension of M = [M]

R is radius so, unit of R = m

and dimension of R = [L]

v is velocity so, unit of v = m/s

and dimension of v = [LT^-1]

now, LHS = dimension of v = [LT^-1]

RHS = dimension of √{2GM/R}

= {dimension of G × dimension of M/dimension of R}½

= {[M^-1L^3T^-2][M]/[L]}½

= [LT^-1]

hence, LHS = RHS

so, formula is dimensionally correct.

Answer 2

Answer:

(ii) 2x2y + (- 4x2y) + 6x2y + (- 5x2y)

= 2x2y - 4x2y + 6x2y - 5x2y

= (2 - 4 + 6 - 5)x2y

= (8 - 9)x2y

= -x2y