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  1. Class 9
  2. Chapter 10 Class 9 - Gravitation

Transcript

Question 2 Page 138 Why is weight of an object on the moon 1/6 th its weight on the earth? Let mass of an object = m Weight on Earth Let Mass of earth = ME = 5.98 Γ— 1024 kg Radius of earth = RE = 6.37 Γ— 106 m , Weight on earth = WE = (〖𝐺𝑀〗_𝐸 π‘š)/〖𝑅_𝐸〗^2 Weight on Moon Let Mass of moon = MM = 7.36 Γ— 1022 kg Radius of moon = RM = 1.74 Γ— 106 m Weight on moon = WM = (〖𝐺𝑀〗_𝑀 π‘š)/〖𝑅_𝑀〗^2 Now (π‘Šπ‘’π‘–π‘”β„Žπ‘‘ π‘œπ‘› π‘šπ‘œπ‘œπ‘›)/(π‘Šπ‘’π‘–π‘”β„Žπ‘‘ π‘œπ‘› π‘’π‘Žπ‘Ÿπ‘‘β„Ž) = π‘Š_𝑀/π‘Š_𝐸 = (〖𝐺𝑀〗_𝑀 𝑀)/〖𝑅_𝑀〗^2 Γ· (〖𝐺𝑀〗_𝐸 𝑀)/〖𝑅_𝐸〗^2 = (〖𝐺𝑀〗_𝑀 𝑀)/〖𝑅_𝑀〗^2 Γ— 〖𝑅_𝐸〗^2/(〖𝐺𝑀〗_𝑀 𝑀) = (𝑀_𝑀 Γ— 〖𝑅_𝐸〗^2)/(𝑀_𝐸 Γ— 〖𝑅_𝑀〗^2 ) Putting values = (7.36 Γ— γ€–10γ€—^22 Γ— ( 6.37 Γ—γ€– 10γ€—^6 )^2)/(5.98 Γ— γ€–10γ€—^(24 )Γ— (1.74 Γ— γ€–10γ€—^6 )^2 ) = (7.36 Γ— γ€–10γ€—^22 Γ— (6.37)^2 Γ— γ€–10γ€—^12)/(5.98 Γ— γ€–10γ€—^(24 ) Γ— (1.74)^2 Γ— γ€–10γ€—^12 ) = (7.36 Γ— (6.37)^2 )/(5.98 Γ— γ€–10γ€—^(2 ) Γ— (1.74)^2 ) = (7.36 Γ— 40.57)/(5.98 Γ— 100 Γ— 3.02) = 298.59/1805.9 β‰ˆ1/6 Thus, π‘Š_𝑀 = 1/6 π‘Š_𝐸 ∴ Weight of an object on the moon is 1/6 of it’s weight on the earth.

About the Author

Davneet Singh's photo - Teacher, Computer Engineer, Marketer
Davneet Singh
Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 9 years. He provides courses for Maths and Science at Teachoo.