Question

If the radius of earth were to shrink by $1$% its mass remaining the same, the acceleration due to gravity on the earth's surface would

• A. Increased by $1$%
• B. Increased by $2$%
• C. Decreased by $2$%
• D. Decreased by $1$%

Answer 1

Answer: (C)

Decreased by $2$%

$g=\frac{GM}{R^2}\therefore \frac{△g}{g}=\frac{△m}{m}+2\frac{△R}{R}\Rightarrow \frac{△g}{g}\times 100=\frac{△m}{m}\times 100+2\frac{△R}{R}\times 100$

Given that

$\Rightarrow \frac{△R}{R}\times 100=-1\%\Rightarrow \frac{△m}{m}\times 100=0\therefore \frac{△g}{g}\times 100=0+2\times (-1)$

$\Rightarrow -2\%$