Question

If radius of the earth were to shrink by 1%, its mass remaining the same, g would decrease by nearly__________.

• A. 1%
• B. 2%
• C. 3%
• D. 4%

Answer 1

Answer: (B)

2%

If mass of the planet remains the same then we can say that

$g_{surface}\alpha \frac{1}{r^2}$

taking log both the sides we get

ln(g) = ln(k)- 2ln(r)

differentiating both sides we get

$\frac{\delta g}{g}=-2\frac{\delta r}{r}$

if $\frac{\delta r}{r}$ = 1 %

then |$\frac{\delta g}{g}$| = 2 %