Question

Value of G on surface of moon

Answer 1

Answer:

The "value of G" on the 'surface of the moon' is 1.625 $\frac{m}{s^{2}}$

Explanation:

• The "acceleration due to gravity" is the acceleration gained by a 'freely falling body' due to gravitational force exerted on it.
• Denoted by the letter g, it depends on the mass of the object (M), distance from the centre of the mass (r), and the gravitational constant G (universal gravitational constant

                      G$=6.673 \times 10^{-11} N m^{2} / k g^{2}$

                     $\mathrm{g}=\frac{\mathrm{GM}}{r^{2}}$

• The value of g is approximately a constant on the earth’s surface but differs on the moon’s surface because the moon’s mass and radius vary.

• Mass of the moon =$7.35 \times 10^{22} \mathrm{kg}$
• Radius of the moon =$1.74 \times 10^{6} \mathrm{m}$

           G=$6.673 \times 10^{-11} \mathrm{N} \mathrm{m}^{2} / \mathrm{kg}^{2}$

Upon substituting,

                 $g=\frac{G M}{r^{2}}$

         g=$\frac{\left(6.673 \times 10^{-11} N \frac{\mathrm{m}^{2}}{\mathrm{kg}^{2}}\right)\left(7.35 \times 10^{22} \mathrm{kg}\right)}{\left(1.74 \times 10^{6} \mathrm{m}\right)^{2}}=1.620 \frac{\mathrm{m}}{\mathrm{s}^{2}}$

So, the "value of g "on moon’s surface = $1.620 \frac{\mathrm{m}}{\mathrm{s}^{2}}$