Question

If the radius of Earth shrinks by 1.5%, mass remaining the same, then how would the value of acceleration due to gravity change?
1. 2%
2. -2%
3. 3%
4. -3%

Answer 1

Answer on Question 48977, Physics, Astronomy — Astrophysics

If the radius of Earth shrinks by 1.5%, mass remaining the same, then how would the value of acceleration due to gravity change? 1. 2% 2. -2% 3. 3% 4. -3%

Solution

Acceleration is

$g=\frac{GM}{R^{2}}$

Hence, decreasing radius on 1.5 % will lead to increasing of gravity on surface:

$\frac{g_{1}}{g}=\frac{R^{2}}{R_{1}^{2}}=\frac{1}{0.985^{2}}\approx 1.03$

Acceleration will increase on 3 %. Answer is 3. 3%.

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