Average density of the earth:

Question

Average density of the earth: (A) does not depend on g . (B) is a complex function of g . (C) is directly proportional to g . (D) is inversely proportional to g .

Tardigrade Admin · Accepted Answer

Acceleration due to gravity, g=(G M/R2), where M=((4/3) π R3)ρ ∴ g=(4 G/3)(π R3/R2)ρ Longrightarrow g=((4 G π R/3))ρ (ρ = a v e r a g e d e n s i t y) Longrightarrow g propto ρ or ρ propto g

Q. Average density of the earth:

does not depend on $g$ .

is a complex function of $g$ .

is directly proportional to $g$ .

is inversely proportional to $g$ .

Acceleration due to gravity, $g = \frac{GM}{R ^{2}},$ where $M = (\frac{4}{3} π R^{3}) ρ$
$∴ g = \frac{4 G}{3} \frac{π R ^{3}}{R ^{2}} ρ$
$⟹ g = (\frac{4 G π R}{3}) ρ (ρ = a v er a g e d e n s i t y)$
$⟹ g \propto ρ$ or $ρ \propto g$

Q. Average density of the earth:

does not depend on g .

is a complex function of g .

is directly proportional to g .

is inversely proportional to g .

Acceleration due to gravity, g=R2GM​, where M=(34​πR3)ρ ∴g=34G​R2πR3​ρ ⟹g=(34GπR​)ρ(ρ=averagedensity) ⟹g∝ρ or ρ∝g

does not depend on $g$ .

is a complex function of $g$ .

is directly proportional to $g$ .

is inversely proportional to $g$ .

Acceleration due to gravity, $g = \frac{GM}{R ^{2}},$ where $M = (\frac{4}{3} π R^{3}) ρ$
$∴ g = \frac{4 G}{3} \frac{π R ^{3}}{R ^{2}} ρ$
$⟹ g = (\frac{4 G π R}{3}) ρ (ρ = a v er a g e d e n s i t y)$
$⟹ g \propto ρ$ or $ρ \propto g$