Question

If the density of earth increases by 20% and radius decreases by 20% then the new value of ''g'' on the surface of earth will be:

• A. $0.8$ g
• B. $0.90$ g
• C. $0.96$ g
• D. g

Answer 1

The correct option is C $0.96$ g

we know,

$g\propto dR$

$\frac{g}{g^{\prime }}=\frac{d}{d^{\prime }}\times \frac{R}{R^{\prime }}$

$=\frac{100}{120}\times \frac{100}{80}$

$\Rightarrow \frac{g}{g^{\prime }}=\frac{25}{24}$

$\therefore g^{\prime }=\frac{24}{25}g$

$\Rightarrow g^{\prime }=0.96g$