Question

If Radius of Earth is increase by 5% and it's
mass is Decrease by 2% find the chance of %in value of g​

Answer 1

hi .....

answer is follow......

Percentage decrease in value of 'g' -

\frac{\Delta g}{g}\times 100\: ^{0}\! \! /\! _{0}=\frac{d}{R}\times 100\: ^{0}\! \! /\! _{0}

\Delta g\rightarrowVariation in 'g'

R\rightarrowRadius

g\rightarrow 9.8\, m/s^{2}

- wherein

rate of decrease of gravity outside the earth (h<<R) is double of that of inside the earth.

g=\frac{GM}{R^{2}}\Rightarrow \frac{dg}{g}=-2\frac{dR}{R}

If \frac{dR}{R} =-1\%

\Rightarrow \frac{dg}{g} =+2\%

\therefore g will increase by 2% .

I hope help to you....

Answer 2

mg=Gmm/r²

so g= GM/R²

now radius increased 5%of earth earlier radius .

n decrease 2% so

g'=[ G(m-2m/100)]/{R+5R/100}²