Question

If the mass of the earth increases by $80\%$ and radius of the earth increases by $40\%$ then the percentage charge in acceleration due to gravity on the surface of radius of earth is (where $g_s=\frac{GM}{R^2},M=$ mass of earth and $R=$ radius of earth})

• A. zero
• B. $+8.16\%$
• C. $-8.16\%$
• D. $160\%$

Answer 1

The correct option is C $-8.16\%$

As per question final radius = 1.4 times initial radius

And final mass =1.8 times initial mass

Using proportionality we can write final g${}_s$= $\frac{1.8}{1.96}$ times initial g${}_s$

Thus acceleration due to gravity decrease by approximately 8.16%

So,C is a correct option.