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Please solve this and explain it to me! Thanks TEST YOUR UNDERSTANDING.docx

rtodd884
8. Feb 2023
Please solve this and explain it to me! Thanks TEST YOUR UNDERSTANDING.docx
Please solve this and explain it to me! Thanks TEST YOUR UNDERSTANDING.docx
Please solve this and explain it to me! Thanks TEST YOUR UNDERSTANDING.docx
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Please solve this and explain it to me! Thanks TEST YOUR UNDERSTANDING.docx

  1. Please solve this and explain it to me! Thanks TEST YOUR UNDERSTANDING OF SECTION 13.2 Rank the following hypothetical planets in order from highest to lowest value of g at the surface: (i) mass 2 times the mass of the earth, radius = 2 times the radius of the earth; (ii) mass = 4 times the mass of the earth, radius 4 times the radius of the earth; (iii) mass-4 times the mass of the earth, radius 2 times the radius of the earth; (iv) mass = 2 times the mass of the earth, radius = 4 times the radius of the earth. I Solution Acceleration due to gravity on the earth's surface g = 9.8 m/s 2 Let the mass of the earth be M Let the radius of the earth be R Acceleration due to gravity at the earth's surface is given by g = G M / R 2 ............ ( 1 ) ( i ) Here mass M1 = 2 M , radius R1 = 2 R Then acceleration due to gravity g1 = G M1 / R1 2 g1 = G * 2 M / ( 2 R ) 2 = 2 G M / 4 R 2 = G M / 2 R 2 = g / 2 = 4.9 m/s 2 ( ii ) Mass M2 = 4 M , radius R2 = 4 R
  2. Acceleration due to gravity g2 = G * M2 / R2 2 g2 = G * 4 M / ( 4 R ) 2 = 4 G M / 16 R 2 = G M / 4 R 2 = g / 4 = 2.45 m/s 2 ( iii ) Here Mass M3 = 4 M , radius R3 = 2 R Acceleration due to gravity g3 = G * M3 / R3 2 g3 = G * 4 M / ( 2 R ) 2 = 4 G M /4 R 2 = G M / R 2 = g = 9.8 m/s 2 ( iv ) Here mass M4 = 2 M , radius R4 = 4R Acceleration due to gravity g4 = G M4 / R4 2 g4 = G * 2 M / ( 4 R ) 2 = 2 G M / 16 R 2 = G M / 8 R 2 = g / 8 = 1.225 m/s 2 From above calculations , we can observe that case ( iii ) has highest value of g , while case ( iv ) have lowest value Planets with g value in order of highest to lowest is ( iii ) , ( i ) , ( ii ) and ( iv )
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