Gravitation Question 218
Question: If the radius of the earth decreases by 10%, the mass remaining unchanged, what will happen to the acceleration due to gravity?
Options:
A) Decreases by 19%
B)Increases by 19%
C)Decreases by more than 19%
D)Increase by more than 19%
Show Answer
Answer:
Correct Answer: D
Solution:
- $ [g=\frac{GM}{R^{2}}] $ (i) $ [g’=\frac{Gm}{{{\left( \frac{90}{100}R \right)}^{2}}}=\frac{100}{81}-\frac{GM}{R^{2}}] $ (ii) From Eqs. (i) and (ii), $ [g’=\frac{100}{81}g\Rightarrow \frac{g’}{g}=\frac{100}{81}] $ $ [\frac{g’}{g}-1=\frac{100}{81}-1] $ $ [\therefore \Delta g=\frac{19}{81}g=23%] $ of g. So increase is more then 19% of g.
