State acceleration due to gravity (g)
Scenario
Agar aap chhat se ek pathar phenko, toh neeche pahunchte pahunchte uski speed badh jati hai.
Raftaar lagataar badh rahi hai, iska matlab acceleration hai. Par yeh acceleration kitna hai aur kaise fix hota hai?
Mental model
Earth ek speed booster hai jo har girti hui cheez ki speed har second badhati rehti hai.
Jab koi cheez free fall karti hai, tab earth usko kheenchti hai. Force lagne par uski velocity mein jo continuous badhotari (increase) hoti hai, use acceleration due to gravity (g) kehte hain.
Explanation
Hum jante hain ki force lagne se motion mein badlav aata hai. Jab object free fall kar raha hota hai, toh earth ki gravity uspar force lagati hai, jisse uski velocity har second change hoti hai. Velocity ke iss change hone ko hi acceleration kehte hain.
Kyunki yeh acceleration earth ke gravitational force ki wajah se ho raha hai, isko 'acceleration due to gravity' kaha jata hai. Ise small 'g' se denote karte hain. Iska unit wahi hota hai jo normal acceleration ka hota hai, yani m/s^2.
Earth ki surface par g ki standard value 9.8 m/s^2 maani jati hai. Iska matlab hai ki agar koi cheez free fall kar rahi hai, toh uski downward speed har second 9.8 m/s se badh jayegi. Pehle second mein 9.8 m/s, doosre mein 19.6 m/s, aur issi tarah.
Ek aur zaroori baat: g ka formula GM/R^2 hota hai, isme girne wale object ka mass (small m) nahi hota. Isliye, ek pathar ho ya feather, vacuum mein dono par 9.8 m/s^2 ka hi acceleration lagta hai.
Worked example
Problem: Why does a 10 kg iron ball and a 1 kg wood ball dropped from the same height in vacuum reach the ground at the same time?
- Acceleration due to gravity ka relation formula g = GM/R^2 se nikalta hai, jahan M Earth ka mass hai.
- Is formula mein girne wale object ka mass m hai hi nahi. Dono balls ke liye g same hai.
Answer: Because the acceleration due to gravity (g) is independent of the mass of the falling object, both experience the same acceleration and reach the ground together.
Problem: What is the value of acceleration due to gravity on the surface of the Earth, and what does this number physically mean?
- Hamein standard value likhni hai jo experiment aur formula se aati hai.
- Iska meaning samajhna hai: har ek second girne par, object ki speed itne factor se badh jayegi.
Answer: The value is 9.8 m/s^2. It means the downward velocity of a free-falling object increases by 9.8 m/s every second.
Key points
- Independent of Object's Mass: The value of g is independent of the falling object's mass; it depends solely on the Earth's mass and radius.
- Value on Earth: The standard value is 9.8 m/s^2, though 10 m/s^2 is sometimes used to simplify numerical calculations.
Common mistakes
- Confusing G and g: Capital G (Universal Gravitational Constant) poore universe mein same rehta hai. Small g (acceleration due to gravity) planet to planet, aur height ke sath change hota hai.
Recall questions
- What is the unit of acceleration due to gravity?
- What is the standard value of acceleration due to gravity (g) on Earth?
- Does the value of g remain exactly the same everywhere on Earth?
Questions & answers
What is the acceleration of free fall?
The acceleration of free fall is the constant acceleration produced in a body when it falls under the influence of gravitational force alone. On Earth, its average value is 9.8 m/s^2.
Approach: Define it first, then mention its numerical value on Earth to be thorough.
Why is the value of g greater at the poles than at the equator?
Because the Earth is an oblate spheroid, making the poles closer to the center of the Earth.
Approach: Use g = GM/R² and relate it to the Earth's radius.
Continue learning
Previous: Define free fall