When the value of acceleration due to gravity 'g' becomes g divided by 3 | PGMN Solutions

Описание: When the value of acceleration due to gravity 'g' becomes g divided by 3 above surface of height 'h', then relation between 'h' and 'R' is (R = radius of earth)
(A) h = R divided by square root of 3 minus 1
(B) h = square root of 3 divided by R
(C) h = (square root of 2 minus 1) times R
(D) h = (square root of 3 minus 1) times R
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🚀 Step-by-Step Solution to Solve This Question 🚀
📌 Chapter: Gravitation
📌 Topic: Variation of gravity with height

🔹 Step 1: Understand the gravity-height relation.
The acceleration due to gravity at a height 'h' above Earth's surface is given by:
g at height = g times R squared divided by (R plus h) squared

🔹 Step 2: Apply the condition given in the question.
It is given that g at height = g divided by 3
So:
g divided by 3 = g times R squared divided by (R plus h) squared

🔹 Step 3: Simplify the equation.
Cancel g from both sides:
1 divided by 3 = R squared divided by (R plus h) squared
Take reciprocal on both sides:
3 = (R plus h) squared divided by R squared
Take square root:
Square root of 3 = (R plus h) divided by R
So: R plus h = R times square root of 3
Therefore, h = R times square root of 3 minus R = R times (square root of 3 minus 1)

🔹 Step 4: Match with options.
This matches with Option (D)

✅ Final Answer: (D) h = (square root of 3 minus 1) times R 🚀
🔥 Pro Tip: When gravity is reduced by a fraction at a height, always apply the inverse square law for accurate height estimation!


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