Question

Find the acceleration due to the gravity of the moon at a point 1000 km above the moon's surface. The mass of the moon is 7.4x10²² kg and its radius is 1740 km.

Answer 1

Thanks for asking the question!

ANSWER::

Acceleration due to gravity of moon,

= GM / (R +h)²

= (6.67 x 10⁻¹¹ x 7.4 x 10²²) / (1740 + 1000)² x 10⁶

= (49.358 x 10¹¹) / (2740 x 2740 x 10⁶)

= (49.358 x 10¹¹) / (0.75 x 10¹³)

= 65.8 x 10⁻²

= 0.65 m/s²

Hope it helps!

Answer 2

$\underline \bold{Given:-}$

Radius of moon (R) = 1740 km = 1740 × 10^3 m

Distance of point from moon's surface (r) =1000km = 1000 × 10^3 m

Mass of moon = $7.4 \times {10}^{22} \: kg$

$\underline \bold{Solution:-}$

Acceleration due to gravity of moon

$= \frac{GM}{ {(R + r)}^{2} }$
$= \frac{(6.67 \times {10}^{ - 11} \times 7.4 \times {10}^{22} )}{ {(1740 \times {10}^{3} + 1000 \times {10}^{3} )}^{2} } \\ \\ = \frac{(49.358 \times {10}^{22 - 11} )}{ {2740}^{2} \times {10}^{6} } \\ \\ = \frac{49.358 \times {10}^{11} }{ 7507600 \times {10}^{6} }$
$= 65.8 \times {10}^{ - 2} \\ \\ = 0.658 \: m \: {sec}^{ - 1}$