Question

Show that weight of an object on moon is 1/6 of its weight on earth.(given :mass of earth = 5.98 * 10 raised to 24 kg,mass of moon 7.36 *10 raised to 22 kg radius of earth 6.37 * 10 raised to 6m radius of the moon 1.74 * 10 raised to 6m

Answer 1

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 = 7.36 × 10²² kg

R_m = 1.74 × 10⁶ m

So, g_m = GM_m/R_m²

For earth,

M_e = 5.98 × 10²⁴ kg

R_e = 6.37 × 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 = 0.16

=> g_e = g_m/0.16 ≈ 6g_m