Question

solve this please please please please​

Answer 1

Answer:

Let a body P of mass m be situated at a depth h below the earth's surface.

The gravitational force of attraction on a body inside a spherical shell is always zero. Therefore, the body P experiences gravitational attraction only due to the inner solid sphere. The mass of this sphere is

M

′

=volume×density=

3

4

π(R

e

−h)

3

ρ

where ρ is mean density of the earth. Therefore, according to Newton's law of gravitation, the force of attraction on the body P is

(R

e

−h)

2

GM

′

m

=G

(R

e

−h)

2

3

4

π(R

e

−h)

3

ρm

=

3

4

πG(R

e

−h)ρm

This force must be equal to the weight of the body mg

′

, where g

′

is the acceleration due to gravity at a depth h below the surface of the earth. Thus,

mg

′

=

3

4

πG(R

e

−h)ρm....(i)

Similarly, if a body be at the surface of the earth (h=0) where acceleration due to gravity is g, then

mg=

3

4

πGR

e

ρm....(ii)

Dividing eq.(i) by (ii) we have

⇒

g

g

′

=

R

e

R

e

−h

⇒g

′

=g(1−

R

e

h

)