The mass of a planet is 1/10 th that of the earth and its diameter is half that of the earth. The acceleration due to gravity on that planet is:

To find the acceleration due to gravity on the planet, we start by writing down the formula for the acceleration due to gravity ($g$) on the surface of any spherical celestial body:

$g=\frac{GM}{R^2}$

where:
• $G$ is the universal gravitational constant,
• $M$ is the mass of the body, and
• $R$ is the radius of the body.

For the Earth, we have:

$g_e=\frac{G{M}_e}{{R_e}^2}=9.8{\text{m s}}^{-2}$

Now, let us consider the parameters of the planet in terms of Earth's parameters:
• The mass of the planet ($M_p$) is one-tenth that of the Earth:
$M_p=\frac{M_e}{10}$
• The diameter of the planet is half that of the Earth, which means its radius ($R_p$) is also half that of the Earth:
$R_p=\frac{R_e}{2}$

Substituting these expressions into the formula for the acceleration due to gravity on the planet ($g_p$):

$g_p=\frac{G{M}_p}{{R_p}^2}$

Substitute $M_p$ and $R_p$ into the equation:

$g_p=\frac{G\left(\frac{M_e}{10}\right)}{{\left(\frac{R_e}{2}\right)}^2}$

Simplify the denominator:

$g_p=\frac{G{M}_e}{10}\times \frac{4}{{R_e}^2}$

Rearrange the terms to express $g_p$ in terms of $g_e$:

$g_p=\frac{4}{10}\left(\frac{G{M}_e}{{R_e}^2}\right)$

$g_p=0.4g_e$

Given that the acceleration due to gravity on the Earth is $g_e=9.8{\text{m s}}^{-2}$, we calculate:

$g_p=0.4\times 9.8=3.92{\text{m s}}^{-2}$

Therefore, the acceleration due to gravity on the planet is 3.92 m s^–2.