Question

If the radius of earth shrinks by $2.4\%$ mass remaining same then the acceleration due to gravity would changes to.

• A. $2.2\%$
• B. $1.2\%$
• C. $4.8\%$
• D. $3.2\%$

Answer 1

Answer: (C)

$4.8\%$

$\because g=\frac{GM}{R^2}$
$\therefore \frac{\Delta g}{g}=-\frac{2\Delta R}{R}$ [As G, M are constants]
$=-2\times \left(\frac{-2.4}{100}\right)=\frac{2\times 2.4}{100}$
So, $\frac{\Delta g}{g}\times 100=\frac{4.8}{100}\times 100=4.8\%$
Hence, percentage increase in the value of g is $4.8\%$.