Question

If the density of the earth is doubled keeping its radius constant then acceleration due to gravity will be

• A. $2.45{ms}^{-2}$
• B. $4.9{ms}^{-2}$
• C. $9.8{ms}^{-2}$
• D. $19.6{ms}^{-2}$

Answer 1

The correct option is D $19.6{ms}^{-2}$

Acceleration due to gravity $g=GM/R^2$ ---------------$\left(1\right)$
The radius is constant, volume also constant$.$
If volume is constant$,$ density is proportional to mass$(v=m/\rho )$
The density is doubled, the mass is also doubled. $(M^{\prime }=2M)$
The new acceleration due to gravity $g^{\prime }=G{M}^{\prime }/R^{\prime 2}$
Put the value $M^{\prime }=2M$ and $R^{\prime }=R$
$g^{\prime }=G\left(2M\right)/R^2$
$g^{\prime }=2GM/R^2$ --------------$\left(2\right)$
Substituting equations $\left(1\right)$ and $\left(2\right),$ we get
$g^{\prime }=2g$
$g=9.8m/s^2$
$g^{\prime }=2\times 9.8=19.6m/s²$

Hence,

option $\left(D\right)$ is correct answer.