Gravitation Question 3
Question 3 - 2024 (27 Jan Shift 1)
The acceleration due to gravity on the surface of earth is $g$. If the diameter of earth reduces to half of its original value and mass remains constant, then acceleration due to gravity on the surface of earth would be :
(1) $g / 4$
(2) $2 g$
(3) $g / 2$
(4) $4 g$
Show Answer
Answer: (4)
Solution:
$g=\frac{GM}{R^{2}} \Rightarrow g \propto \frac{1}{R^{2}}$
$\frac{g _2}{g _1}=\frac{R _1^{2}}{R _2^{2}}$
$g _2=4 g _1\left(R _2=\frac{R _1}{2}\right)$
