Question

Aplanet has a mass of eight times the mass of earth and density is also equal to eight times the average density of the earth.If g be the acceleration due to earth's gravity on its surface, then acceleration due to gravity on planet's surface will be

• A. 2 g
• B. 4 g
• C. 8 g
• D. 16 g

Answer 1

The correct option is C

8 g

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

$M=\frac{4}{3}\pi R^{3}d$

$\therefore$ $R={\left(\frac{3M}{4\pi d}\right)}^{\frac{1}{3}}$

Substituting in Eq.(1) we have,

$g=GM{\left(\frac{4\pi d}{3M}\right)}^{\frac{2}{3}}$

or $g\propto M^{\frac{1}{3}}{d}^{\frac{2}{3}}$

$\therefore$ $g_{planet}=g\left(8{)}^{\frac{1}{3}}\right(8{)}^{\frac{21}{3}}=8g$