Question

4: a) Dimensionally, Check correctness of escape velocity, v= V(2GM/R),
where G is universal gravitation constant, M is mass of planet, and
R is radius of planet.
b) What are the dimensions of a and b in relation: F= a + bx2, where
Fis force and x is distance.​

Answer 1

Answer:

you mean, we have to check  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.

Explanation: