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Maharashtra Class 10 Answered

What would be the value of 'g' on the surface of the earth if its mass was twice as large and radius half of what it is now?
Asked by omkarzite15 | 05 Jul, 2019, 07:40: PM
answered-by-expert Expert Answer
We know, 
acceleartion due to gravity is, 
g = GM/R2 ... (*) 
where, 
G - universal gravitational constant
M - mass of the earth
R - radius of the earth. 
 
If the mass is twice then 
M = 2M 
Rradius is halved 
thus, 
R =R/2
Substituting in equation (*) 
 
 
g subscript c equals fraction numerator G left parenthesis 2 M right parenthesis over denominator open parentheses begin display style bevelled R over 2 end style close parentheses squared end fraction space equals space fraction numerator 2 G M over denominator begin display style bevelled R squared over 4 end style end fraction space space... space left parenthesis w h e r e space g space i s space t h e space c h n a g e d space v a l u e space o f space a c c e l e r a t i o n space d u e space t o space g r a v i t y right parenthesis space t h u s comma space g subscript c space equals space fraction numerator 8 space G M over denominator R squared end fraction equals space 8 open parentheses fraction numerator G M over denominator R squared end fraction close parentheses g subscript c space equals space 8 g space 
 
 Thus, 
g =9.8 m/s2 
 
gc = 8 x 9.8 = 78.4 m/s2 
Answered by Shiwani Sawant | 06 Jul, 2019, 02:47: PM

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