If R is the radius of the earth and g the acceleration due to gravity on the earth's surface, the mean density of the earth is

πRg/12G
4πG/3gR
3πR/4gG
3g/4πRG

Question

If R is the radius of the earth and g the acceleration due to gravity on the earth-s surface- the mean density of the earth is-Rg-12G4-G-3gR3-R-4gG3g-4-RG

Toppr Admin · Accepted Answer

We know thatg-GMR2Also- density -mass-xD7-volumeM-density-xD7-volumeM-P-xD7-4-x3C0-R33R2-P-xD7-4-x3C0-R3Put value of m in g-GMR2P-3g4-x3C0-RG

If R is the radius of the earth and g the acceleration due to gravity on the earth's surface, the mean density of the earth isπRg/12G4πG/3gR3πR/4gG3g/4πRG

We know thatg=GMR2Also, density =mass×volumeM=density×volumeM=P×4πR33R2=P×4πR3Put value of m in g=GMR2P=3g4πRG

If R is the radius of the earth and g the acceleration due to gravity on the earth's surface, the mean density of the earth is

πRg/12G
4πG/3gR
3πR/4gG
3g/4πRG

We know that
$g = \frac{G M}{R^{2}}$
Also, density $= m a s s \times v o l u m e$
$M = d e n s i t y \times v o l u m e M = P \times \frac{4 π R^{3}}{3 R^{2}} = P \times \frac{4 π R}{3}$
Put value of m in $g = \frac{G M}{R^{2}} P = \frac{3 g}{4 π R G}$