Question

On the moon surface the acceleration due to gravity is 1.67 ms ^-2 . If the radius of the moon is 1.74 ×10^6 m . Calculate the mass of the moon . ( G = 6.67 × 10 ^-11 Nm^2 / kg ^2 )​

Answer 1

Answer:

7.5 × 10^22 Kg

Explanation:

We have:

• Acceleration due to gravity (g) = 1.67 m/s².
• Radius of moon (R) = 1.74 × 10^6 m.
• Gravitational constant (G) = 6.67 × 10^-11 Nm²/Kg²

To find:

• Mass of the moon (M)

Solution:

Using the formula,

=> g = GM/R²

We get,

=> M = gR²/G

Substituting,

>> M = (1.74 × 10^6)^2 × 1.67/6.67 × 10^-11

>> M = 5.05 × 10^12/6.67 × 10^-11

>> M = 5.05 × 10^23/6.67

>> M = 0.75 × 10^23 Kg

∴ M = 7.5 × 10^22 Kg