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Question No. 14
English
The acceleration due to gravity on surface of moon is 9m. The moon is assumed to be sphere of uniform mass density p and radius Rm. The density of moon is related to
its acceleration due to gravity by relation
4-GR
4.GR
P-
39m
P
4-GR
3.GR
Ag

Answer 1

Answer:

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Answer 2

Given : The acceleration due to gravity on surface of moon is  $g_m$

The moon is assumed to be sphere of uniform mass density ρ and radius $R_m$

To Find :  The density of moon is related to  its acceleration due to gravity by relation

Solution:

$g_m$ = GM/ $R_m$²

density = Mass/Volume

Volume = (4/3)π$R_m$³

=> ρ = M/ (4/3)π$R_m$³

=> M = ρ (4/3)π$R_m$³

$g_m$ = GM/$R_m$²

=>$g_m$  = Gρ (4/3)π$R_m$³/ R²

=>$g_m$ = G ρ (4/3)π$R_m$

=> ρ  =  3$g_m$/4πG$R_m$

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