question_answer

A particle is taken to a height R above the earths surface, where R is the radius of the earth. The acceleration due to gravity there is

A)  \[2.45\text{ }m/{{s}^{2}}\]         

B)  \[4.9\text{ }m/{{s}^{2}}\]

C)  \[9.8\text{ }m/{{s}^{2}}\]           

D)  \[19.6\text{ }m/{{s}^{2}}\]

Correct Answer: A

Solution :

  \[{{R}^{|}}=2R\] We know \[{{g}_{s}}=\frac{GM}{{{R}^{2}}}\]           ________ (1) \[{{g}_{h}}=\frac{GM}{{{(R+h)}^{2}}}=\frac{GM}{{{(2R)}^{2}}}\] \[\Rightarrow \]\[{{g}_{h}}=\frac{GM}{4{{R}^{2}}}\]                        __________ (2) From (1) and (2), we get \[{{g}_{h}}=\frac{1}{4}g=\frac{9.8}{4}=2.45\,m/{{s}^{2}}\]