Gravitation Question 3
Question 3 - 2024 (27 Jan Shift 1)
The acceleration due to gravity on the surface of earth is $\mathrm{g}$. 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) $2 \mathrm{~g}$
(3) $g / 2$
(4) $4 \mathrm{~g}$
Show Answer
Answer: (4)
Solution:
$\mathrm{g}=\frac{\mathrm{GM}}{\mathrm{R}^{2}} \Rightarrow \mathrm{g} \propto \frac{1}{\mathrm{R}^{2}}$
$\frac{\mathrm{g}{2}}{\mathrm{~g}{1}}=\frac{\mathrm{R}{1}^{2}}{\mathrm{R}{2}^{2}}$
$\mathrm{g}{2}=4 \mathrm{~g}{1}\left(\mathrm{R}{2}=\frac{\mathrm{R}{1}}{2}\right)$
