Question

If the density of the earth is doubled keeping radius constant, find the new acceleration due to gravity? (g = 9.8 m/s ${}^2$)

• A. 9.8 m/s${}^2$
• B. 19.6 m/s${}^2$
• C. 4.9 m/s${}^2$
• D. 39.2 m/s${}^2$

Answer 1

Answer: (B)

19.6 m/s${}^2$

Acceleration due to gravity $g=\frac{GM}{R^2}$

$=\frac{G\left(\rho \frac{4}{3}\pi R^3\right)}{R^2}$

$\propto \rho$

Thus when density of earth is doubled, the acceleration due gravity also doubles and becomes=$9.8m/s^2\times 2=19.6m/s^2$