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CBSE Class 9 Answered

Explain why the value of g is zero at the centre of the earth
Asked by rohan78378 | 03 Jun, 2018, 08:53: PM
answered-by-expert Expert Answer
The general equation for acceleration due to gravity 'g' is
begin mathsize 12px style straight g space equals space GM over straight r squared end style
Assuming Earth to be a perfect sphere, and considering it's uniform density
we make the following adjustments in the above equation.
 
begin mathsize 12px style straight g space equals space GM over straight r squared Multiplying space and space dividing space the space RHS space by space Volume space apostrophe straight v apostrophe straight g space equals space GM over straight v cross times straight v cross times 1 over straight r squared We space know space that space straight M over straight v space is space density space straight rho Therefore comma straight g space equals fraction numerator straight rho Gv over denominator straight r squared end fraction For space straight a space sphere comma space straight v space equals space 4 over 3 πr cubed. space This space makes straight g space equals space 4 over 3 πr cubed space cross times ρG over straight r squared straight g space equals fraction numerator 4 πrρG over denominator 3 end fraction At space the space centre space of space the space Earth comma space straight r space equals 0 Thus comma space straight g equals 0 end style
Answered by Abhijeet Mishra | 04 Jun, 2018, 02:59: PM

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