Question

Mars has a diameter of approximately $0.5$ times that of earth and mass is $0.1$ times that of earth. The surface gravitational field strength on mars as compared to that of earth is a factor of
A. $0.1$
B. $0.2$
C. $2.0$
D. $0.4$

Answer 1

Hint: In order to solve this question, we should know about gravitational field strength of a planet, Gravitational field strength is a measure of acceleration on a body falling freely under the force of gravity on a planet, we will use the general formula of gravitational field strength and will compare of these two planets mars and earth.

Formula Used:
If $M$ is the mass of a planet and $R$ is the radius of a planet and $G$ be the gravitational constant and $g$ represents the gravitational field strength then $$g={\displaystyle \frac{GM}{R^2}}$$.

Complete step by step answer:
According to the question we have given, assume $M_{mars}(and)M_{earth}$ denote the mass of mars and earth. and $R_{mars}(and)R_{earth}$ denote the radii of these two planets.
$M_{mars}=0.1M_{earth}$
and diameters of two planets can be written as $R={\displaystyle \frac{D}{2}}$ and it is given that
$D_{mars}=0.5D_{earth}$
$\Rightarrow {\displaystyle \frac{D_{mars}}{2}}={\displaystyle \frac{0.5(D_{earth})}{2}}$
$\Rightarrow R_{mars}=0.5R_{earth}$
Now for planet earth using the formula $$g={\displaystyle \frac{GM}{R^2}}$$ we have,
$$g_{earth}={\displaystyle \frac{G{M}_{earth}}{{R_{earth}}^2}}$$
for planet mars we have,
$$g_{mars}={\displaystyle \frac{G{M}_{mars}}{{R_{mars}}^2}}$$
putting the values of parameters we get,
$$g_{mars}={\displaystyle \frac{(0.1)G{M}_{earth}}{{(0.5)}^2{R_{earth}}^2}}$$
$$\Rightarrow g_{mars}={\displaystyle \frac{0.1}{0.25}}{g}_{earth}$$
$$\Rightarrow g_{mars}={\displaystyle \frac{10}{25}}{g}_{earth}$$
$$\therefore g_{mars}=0.4g_{earth}$$

Hence, the correct option is D.

Note: It should be remembered that, the value of acceleration due to gravity on each planet is different and larger the acceleration due to gravity of a planet the more the energy needed to escape the gravitational field of that planet. Free fall means when a body is released to fall under the force of gravity with zero initial velocity.