Acceleration Due to Gravity and its variation: Practice Problem & Solution
If the radius of the earth were to shrink by one percent, its mass remaining the same, the value of \(g\) on the earth’s surface would
Short Solution (Best for NEET):
To solve this problem, we apply the core principles of Acceleration Due to Gravity and its variation. Understanding the underlying formula is key to arriving at the correct answer below:
Since \(g = \frac{GM}{R^2}\), for a small percentage change: \(\frac{\Delta g}{g} \times 100 = -2 \frac{\Delta R}{R} \times 100\). Since \(R\) decreases by \(1%\), \(g\) increases by \(2%\).
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