Calculate weight on earth and moon
Scenario
Agar aap Earth pe 60 kg ka heavy dumbbell utha sakte hain, to moon par wo aapko bohot halka lagega.
Moon par jaakar aapka weight achanak kitna kam ho jata hai, aur kyun?
Mental model
Moon Earth se halka hai, isliye uska pull (gravity) bhi `6` times kamzor hai.
Kyunki moon ka mass Earth se kam hai aur radius bhi chhota hai, uski gravity Earth ki gravity ki lagbhag `1/6`th hoti hai. Isliye jab aap moon par jate hain, aapka mass wahi rehta hai, par weight bilkul `6` guna kam ho jata hai.
Explanation
Weight calculate karne ka basic formula `W = m imes g` hai. Kisi object ka mass `m` fix rehta hai, toh uska weight poori tarah iss baat par nirbhar karta hai ki `g` ki value uss specific planet ya moon par kya hai.
Earth par `g` ki value lagbhag `9.8 m/s^2` hoti hai, isliye yahan object ka weight bhari hota hai. Moon, kyunki earth se size aur mass dono mein chhota hai, uski gravity bahut weaker hoti hai. Moon par `g` ki value earth ki `g` ki value ka sirf `1/6` (ek bata chheh) hissa hoti hai, yani around `1.63 m/s^2`.
Iska seedha sa matlab yeh nikalta hai ki: `Weight of object on moon = 1/6 imes (Weight of object on Earth)`. Agar aap earth par `600 N` ke weight ka pull feel karte hain, toh moon par aap sirf `100 N` feel karenge. Isliye moon walkers hawa mein lambi-lambi chalange maar paate the.
Worked example
Problem: Mass of an object is `10 kg`. What is its weight on earth? What would be its weight on the moon?
- Pehle Earth par weight `W = m imes g` se nikalte hain. Earth ka `g` lagbhag `9.8 m/s^2` hai.
- Ab moon par weight nikalne ke liye Earth ke weight ko `6` se divide karenge.
- Calculation simple hai.
Answer: Weight on earth is `98 N`, and weight on moon is `16.33 N`.
Problem: An astronaut weighs `120 N` on the moon. What is her mass on earth? (Take `g_earth = 10 m/s^2` for simplicity)
- Moon par weight `120 N` hai, toh Earth par usse `6` times zyada hoga.
- Hamein Earth par mass nikalna hai. `W = m imes g` wala formula reverse mein use karenge.
Answer: `72 kg`
Key points
- Moon's Gravity Factor: `g_moon` is approximately equal to `1/6` of `g_earth`.
- Mass Remains Unchanged: Remember that only the weight on the moon becomes `1/6`th of that on Earth; the mass remains exactly the same.
Common mistakes
- Dividing the Mass by 6: Students ko jab moon par details puchi jati hain toh log galti se mass ko bhi `6` se divide kar dete hain. Mass har jagah same hota hai, sirf weight change hota hai.
Recall questions
- By what factor does the weight of an object change when moved from Earth to the Moon?
- What is the relation between weight on the Moon and weight on Earth?
- Does the mass of an object change on the Moon?
Questions & answers
Why is the weight of an object on the moon 1/6th its weight on the earth?
Because the mass and radius of the moon are less than that of the earth, its gravitational pull is weaker. The acceleration due to gravity on the moon is about one-sixth of that on the earth.
Approach: Mention the physical difference (lesser mass and radius of moon) that leads to lesser gravity.
An object weighs 60 N on Earth. What is its weight on the Moon?
10 N
Approach: Weight on Moon = 60 / 6 = 10 N.
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