Question

If two places are at the same height from the mean sea level: One is a mountain and other is in air. At which place will 'g' be greater? State the reason for your answer.

Answer 1

we known acceleration due to gravity on the earth's surface is given by g = GM/R²,

We also know mass = volume × density

Let $\rho$ denotes density and volume of spherical earth, V = 4/3 πR³

So, $g=\frac{4}{3}\pi R\rho G$

A/c to question, two places are at the same height from the mean sea level e.g., R is constant .
Hence, g is directly proportional to density of surface. in case of mountain and air , definitely density of mountain is greater than air .
so, acceleration due to gravity will be greater at mountain.

Answer 2

Explanation:

Let g_pg

p

is the acceleration due to gravity at pole and g_eg

e

acceleration due to gravity at equator.

weight of the object at pole ,W_p=mg_pW

p

=mg

p

weight of the object at equator, W_e=mg_eW

e

=mg

e

a/c to question,

weight of the object at pole > weight of the object at equator.

e.g., m_pg_p > m_eg_em

p

g

p

>m

e

g

e

We know that, g_p > g_eg

p

>g

e

then, m_e > m_pm

e

>m

p

Hence, we can get more sugar at equator.