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Gravitation

Question
CBSEENPH11020814

Suppose the charge of a proton and an electron differ slightly. One of them is –e, the other is (e + Δe). If the net of electrostatic force and gravitational force between two hydrogen atoms placed at a distance d (much greater than atomic size) apart is zero, then Δe is of the order of [Given mass of hydrogen
mh = 1.67 × 10–27 kg]

  • 10–20 C

  • 10–23 C

  • 10–37 C

  • 10–47 C

Solution

C.

10–37 C

Fe = Fg
fraction numerator 1 over denominator 4 πε subscript 0 end fraction fraction numerator increment straight e squared over denominator straight d squared end fraction space equals space Gm squared over straight d squared
9 space straight x space 10 to the power of 9 space left parenthesis increment straight e squared right parenthesis space equals space 6.67 space straight x space 10 to the power of negative 11 end exponent space straight x space 1.67
straight x space 10 to the power of negative 27 end exponent space space straight x space 1.67 space straight x space 10 to the power of negative 27 end exponent
increment straight e squared space equals space fraction numerator 6.67 space straight x space 1.67 space straight x space 1.67 over denominator 9 end fraction space straight x space 10 to the power of negative 74 end exponent
increment straight e almost equal to space 10 to the power of negative 37 end exponent