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Atoms And Molecules

Question
CBSEENSC9006101

Suppose that the two giant planets of the solar system, Jupiter and Saturn, are in the same line as seen from the earth. It happens occasionally that some planets appear in the same line from the earth. Find the total gravitational force due to them on a person of mass 50 kg on the earth. Compare this with the force of gravity on the same person. Could the force due to planets be important?

Solution

The given question has been illustrated in the figure below. 


straight F subscript total space equals space straight F subscript saturn minus 50 end subscript space plus space straight F subscript Jupiter minus 50 end subscript

equals space fraction numerator straight G.50 space cross times space 6 cross times 10 to the power of 26 over denominator left parenthesis 12.8 cross times 10 to the power of 11 space minus space 6.4 cross times 10 to the power of 6 right parenthesis squared end fraction plus fraction numerator straight G.50 cross times 2 cross times 10 to the power of 27 over denominator left parenthesis 6.3 cross times 10 to the power of 11 minus 6.4 cross times 10 to the power of 6 right parenthesis squared end fraction

equals space 6.67 cross times 10 to the power of negative 11 end exponent open square brackets fraction numerator 3 cross times 10 to the power of 28 minus 22 end exponent over denominator 12.8 cross times 12.8 end fraction plus fraction numerator 1 cross times 10 to the power of 29 minus 22 end exponent over denominator 6.3 cross times 6.3 end fraction close square brackets

equals space 6.67 cross times 10 to the power of negative 11 end exponent left square bracket 0.27 cross times 10 to the power of 6 right square bracket

equals space 1.8 space cross times space 10 to the power of negative 5 end exponent space straight N

So comma space the space force space of space gravity space on space 50 space kg space almost equal to space 50 space cross times 9.8 space straight N space equals space 490 space straight N

 
The force due to planets, is very small and hence is negligible.