Question

When the radius of earth is reduced by 1% with out changing the mass, then the acceleration due to gravity will

• A. increase by 2%
• B. decrease by 1.5%
• C. increase by 1%
• D. decrease by 1%

Answer 1

The correct option is A increase by 2%

Let the mass and radius of Earth be $M$ and $R$ respectively. Acceleration due to gravity

$g=\frac{GM}{R^2}$

Now Radius

$R^{\prime }=R-\frac{R}{100}=0.99R$

So acceleration due to gravity

$g^{\prime }=\frac{GM}{{\left(0.99\right)}^2}$

or $g^{\prime }=1.02\frac{GM}{R^2}$

Now change in acceleration due to gravity

$=g^{\prime }-g$

$=(1.02-1)\frac{GM}{R^2}$

$=\left(0.02\right)\frac{GM}{R^2}$

Thus acceleration due to gravity increased by $2$%

$\therefore$ So (a) option is correct answer.