Question

If both the mass and radius of the earth decrease by $1\%$ the acceleration due to gravity on the surface of the earth will

• A. decrease by $1\%$
• B. increase by $1\%$
• C. increase by $2\%$
• D. remain unchanged

Answer 1

The correct option is A decrease by $1\%$

$R\prime \to R-\frac{R}{100}=\frac{99R}{100}$

$M\prime \to M-\frac{M}{100}=\frac{99M}{100}$

$\therefore g\prime =\frac{GM}{R^2}=\frac{G\times 99M\times 100\times 100}{100\times 99R\times 99R}$

$\Rightarrow g\prime =\frac{GM}{\frac{99R^2}{100}}$

$\Rightarrow g\prime =\frac{GM}{R^2}\left(\frac{100}{99}\right)$

$\Rightarrow g\prime =\frac{100}{99}$

$\Rightarrow g\prime =1.0101g$

Thus $g\prime$ decreases by $1\%$