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  • If the mass of the earth is increased by , density is decreased by <img alt="2 \%" src="https://entrancecorne

If the mass of the earth is increased by 1 \%, density is decreased by 2 \% the change in acceleration due to gravity at the surface of earth is
 

Option: 1

1 \%

 


Option: 2

-2%


Option: 3

-1%


Option: 4

None of these


Answers (1)

best_answer

\mathrm{g=\frac{G M}{r^2} \quad} Since the average density of earth \mathrm{\rho=\frac{M}{(4 / 3) \pi r^3} \quad \Rightarrow r=\left(\frac{3 M}{4 \pi \rho}\right)^{1 / 3}}

\mathrm{ \Rightarrow g=\frac{G M}{\left(\frac{3 M}{4 \pi \rho}\right)^{2 / 3}}=G M^{1 / 3}\left(\frac{4 \pi}{3}\right)^{2 / 3} \rho^{2 / 3} }

\mathrm{ \Rightarrow \quad \ln g=\ln \left\{G\left(\frac{4 \pi}{3}\right)^{2 / 3}\right\}+\frac{1}{3} \ln M+\frac{2}{3} \ln \rho }

\mathrm{ \Rightarrow \frac{\delta \mathrm{g}}{\mathrm{g}}=\frac{\delta \mathrm{M}}{\mathrm{M}}+\frac{2}{3} \frac{\delta \rho}{\rho} \quad \Rightarrow \frac{\delta \mathrm{g}}{\mathrm{g}}=\frac{1}{3}(+1 \%)+\frac{2}{3}(-2) \% }

\mathrm{ \Rightarrow-1 \% \text {. } }

Hence option 3 is correct.





 

Posted by

Gautam harsolia

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