Question

V=√2gr is it dimensionally correct or not?

Answer 1

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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.

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Hope it helps !!!

Answer 2

Answer:

$❥\huge\underline\mathfrak\purple{Answer}$

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.