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Laws Of Motion

Question
CBSEENPH11016615

Show that ratio of electric to gravitational interaction between two protons is of the order of 1036.

Solution
The gravitational force between two masses is, 
                    straight F subscript straight g space equals space straight G fraction numerator straight m subscript 1 straight m subscript 2 over denominator straight r squared end fraction 
The electrostatic force between two charges is,
                    straight F subscript straight e space equals space fraction numerator 1 over denominator 4 πε subscript straight o end fraction fraction numerator straight q subscript 1 straight q subscript 2 over denominator straight r squared end fraction 
Therefore, 
straight F subscript straight e over straight F subscript straight g equals fraction numerator begin display style fraction numerator 1 over denominator 4 πε subscript 0 end fraction fraction numerator straight q subscript 1 straight q subscript 2 over denominator straight r squared end fraction end style over denominator straight G begin display style fraction numerator straight m subscript 1 straight m subscript 2 over denominator straight r squared end fraction end style end fraction equals fraction numerator 1 over denominator 4 πε subscript straight o straight G end fraction fraction numerator straight q subscript 1 straight q subscript 2 over denominator straight m subscript 1 straight m subscript 2 end fraction 
For proton: 
Mass of protons, straight m subscript 1 equals straight m subscript 2 equals 1.67 cross times 10 to the power of negative 27 end exponent space kg
Charge on proton, straight q subscript 1 equals straight q subscript 1 equals 1.6 cross times 10 to the power of negative 19 end exponent straight C 
So ratio of electric to gravitational force is, 
straight F subscript straight e over straight F subscript straight g equals fraction numerator 9 cross times 10 to the power of 9 over denominator 6.67 cross times 10 to the power of negative 11 end exponent end fraction open parentheses 1.67 cross times 10 to the power of negative 27 end exponent close parentheses squared over open parentheses 1.6 cross times 10 to the power of negative 19 end exponent close parentheses squared 
   space space almost equal to space 10 to the power of 36