What is meant by acceleration due to gravity? Suppose a planet exists whose mass and radius both are half of that of Earth. Calculate the acceleration due to gravity on the surface of this planet.

(N/A) Acceleration due to gravity is the acceleration produced in a body when it is allowed to fall freely under the influence of gravity alone. The acceleration due to gravity $(g)$ on the surface of a planet is given by the formula $g = \frac{GM}{R^2}$,where $M$ is the mass of the planet and $R$ is its radius.
Given:
Mass of the planet $(M_P)$ = $\frac{M_E}{2}$
Radius of the planet $(R_P)$ = $\frac{R_E}{2}$
Acceleration due to gravity on Earth $(g_E)$ = $9.8 \, m/s^2$
Using the ratio:
$\frac{g_P}{g_E} = \frac{GM_P / R_P^2}{GM_E / R_E^2} = \frac{M_P}{M_E} \times (\frac{R_E}{R_P})^2$
Substituting the values:
$\frac{g_P}{g_E} = \frac{M_E / 2}{M_E} \times (\frac{R_E}{R_E / 2})^2 = \frac{1}{2} \times (2)^2 = \frac{1}{2} \times 4 = 2$
Therefore,$g_P = 2 \times g_E = 2 \times 9.8 \, m/s^2 = 19.6 \, m/s^2$.