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When an object falls freely from some height on the surface of the Earth, a force acts on it due to the gravity of the Earth. It produces acceleration in the object, which is termed acceleration due to gravity.

For example, when a leaf falls from a tree under the effect of gravity, acceleration is produced in it due to gravity.

If 鈥済鈥� is the acceleration due to gravity on the Earth, its value on the Moon is$\frac{\mathbf{g}}{\mathbf{6}}$.

Since the object is thrown upwards, its acceleration equals the negative of acceleration due to gravity.

Thus, acceleration of the object on the Earth, $a=-g$.

Acceleration of the object on the Moon, $a\text{'}=-\frac{g}{6}$.

When an object is thrown vertically upwards on the Earth, with initial velocity u, it reaches a maximum height h. The final velocity of the object becomes zero, i.e., $v=0{\mathrm{ms}}^{-1}$. The equation of motion for the upward motion in this case is

role="math" localid="1643093052085" $\begin{array}{c}{v}^2-u^2=2ah\\ {\left(0\right)}^2-u^2=2\left(-\mathrm{g}\right)h\\ u^2=2gh....\left(i\right)\end{array}$

When an object is thrown vertically upwards on the Moon with initial velocity $u\text{'}$, it reaches a maximum height$h\text{'}$. Thefinal velocity of the object becomes zero, i.e., $v\text{'}=0{\mathrm{ms}}^{-1}$. The equation of motion for the upward motion in this case is

role="math" localid="1643093125181" $\begin{array}{c}{\left(v\text{'}\right)}^2-{\left(u\text{'}\right)}^2=2a\text{'}h\text{'}\\ {\left(0\right)}^2-{\left(u\text{'}\right)}^2=2\left(-\frac{\mathrm{g}}{6}\right)h\text{'}\\ {\left(u\text{'}\right)}^2=\frac{gh\text{'}}{3}....\left(ii\right)\end{array}$

If the object is thrown with the same initial speed on the Earth and the Moon, equations (i) and (ii) become equal.

$\begin{array}{c}2gh=\frac{gh\text{'}}{3}\\ h\text{'}=6h\end{array}$

Thus, if thrown with the same initial speed, the object will go six times higher on the Moon than it would go on the Earth.