JEE Main On 16 April 2018 Question 19
Question: The relative uncertainty in the period of a satellite orbiting around the earth is $ {10^{-2}}. $ If the relative uncertainty in the radius of the orbit is negligible, the relative uncertainty in the mass of the earth is [JEE Main 16-4-2018]
Options:
A) $ 3\times {10^{-2}} $
B) $ {10^{-2}} $
C) $ 2\times {10^{-2}} $
D) $ 6\times {10^{-2}} $
Show Answer
Answer:
Correct Answer: C
Solution:
$ T=2\pi \sqrt{\frac{r^{3}}{GM _{e}}} $
$ T^{2}=\frac{4{{(\pi )}^{2}}r^{3}}{GM} $
$ \ln (T^{2})=ln(\frac{4{{(\pi )}^{2}}r^{3}}{GM}) $
$ \ln (T^{2})=\ln (\frac{4{{(\pi )}^{2}}r^{3}}{G})+\ln (M) $
$ 2\ln (T)=\ln (K)+\ln (M) $
$ 2\frac{\Delta \tau }{T}=\frac{\Delta M}{M} $
$ \frac{\Delta \mu }{M}=2\times {10^{-2}} $
