Question

Find the value of acceleration due to gravity on the surface of the moon. Mass of the moon = 7.35×10²²kg. Radius of the moon = 1.74×10⁶m, G= 6.67×10_¹¹(ten to the power minus eleven)Nm²/kg². Use formula g=Gm/R².​

Answer 1

1.62 m/s² is the required answer.

GIVEN:

• Mass of the moon, M = 7.35 × 10²² kg.

• Radius of the moon , R = 1.74 × 10⁶ m

• Gravitational constant, G = 6.67 × 10^-11 Nm²/kg²

TO FIND:

Acceleration due to gravity on the surface of the moon, g

FORMULA:

Acceleration due to gravity , g = GM / R²

SOLUTION:

g = GM / R²

$g = \frac{6.67 \times {10}^{ - 11} \times 7.35 \times {10}^{22} }{ ({1.74 \times {10}^{6}) }^{2} } \\ \\ = \frac{6.67 \times 7.35 \times {10}^{ - 11} \times {10}^{22} }{1.74 \times 1.74 \times {10}^{12} } \\ \\ = \frac{6.67 \times 7.35 \times {10}^{ 11} \times {10}^{ - 12} }{1.74 \times 1.74} \\ \\ = \frac{49.0245 \times {10}^{ - 1} }{3.0276} \\ \\ = \frac{4.90245}{3.0276} \\ \\ g = 1.619 \\ \\ g = 1.62 \: \frac{m}{ {s}^{2} }$

ANSWER:

Acceleration due to gravity on the surface of the moon is 1.62 m/s²

ACCELERATION DUE TO GRAVITY:

• It varies on different planet.

• It is dependent of mass and radius of the planet.

• The value of g in a planet also varies due to lattitude, depth and rotational effect of the planet.

• Acceleration due to gravity on moon is one sixth of the acceleration due to gravity on Earth.

• Acceleration due to gravity always acts towards the centre of the planet.