Question

assuming the mass of earth to remain constant what is the percentage change in value of g if it radius is reduced that 5%?​

Answer 1

QUESTION-:

assuming the mass of earth to remain constant what is the percentage change in value of g if it radius is reduced that 5%?​

EXPLANATION-:

We know that-:

$\rightarrow \bf\; g=\frac{Gm}{R^2}$

Now after radius is decreased by 5 % ,new radius will be-:

$\rightarrow \bf\; R'=R-\frac{5R}{100}\\\\\rightarrow \bf\; R'=\frac{95R}{100}$

Now let's calculate g'

$\rightarrow \bf\; g'=\frac{Gm}{R'^2}\\\\\rightarrow \bf\; g'=\frac{Gm}{(\frac{95}{100})^2} \\\\\rightarrow \bf\; g'=\frac{g}{(\frac{95}{100})^2}$

Now let's calculate  % change

$\longrightarrow \bf\; Percentage\;change=\frac{g'-g}{g}\times 100$

Putting values-:

$\rightarrow \bf\; Percentage\;change=\frac{\frac{(100)^2}{(95)^2}-g }{g} \\\\\rightarrow \bf\; Percentage\;change=\frac{(100)^2-(95)^2}{(95)^2} \times 100\\\\\rightarrow Percentage\;change=\frac{3900}{361} \\\\\dashrightarrow \boxed{\tt Percentage\;change\approx 10.8\;}$

∴The percentage decrease is 10.8(approx) .