Question

$$\begin{gathered} 9.SHowthattheweightofanobjectonthemoonis\frac{1}{6}thofitsweightontheearth. \\ 12.Whereistheaccelerationduetogravityminimumandmaximumonthesurfaceoftheearth? \end{gathered}$$

Answer 1

Dear student,
Due to the paucity of time, we can solve each of your query in a single thread so post different queries in the different thread.
Answer to question 9 is below,

The acceleration due to gravity is given by,

g = GM/R²

Where, M is the mass of the planet or satellite where ‘g’ is to be found and R is its radius.

For Moon,

M_m = 7.3459 × 10²² kg

R_m = 1.7375 × 10⁶ m

So, g_m = GM_m/R_m²

For earth,

M_e = 5.9721 × 10²⁴ kg

R_e = 6.6375 × 10⁶ m

So,

g_e = GM_e/R_e²

Now,

g_m/g_e = (M_m R_e²)( M_e R_m²)

Plugging in the values we get,

g_m/g_e = 0.17

=> g_e = g_m/0.17 = 5.9 g_m

Or, g_e ≈ 6gm

Weight on earth= mg_e
weight on Moon= mg_m =mg_e /6
Hence proved that the weight on the Moon is one-sixth of the weight on the Earth.

Regards