Question

show that the gravitational field and potential at any point on the surface of earth are g and gR respectively .the earth may be assumed to be a sphere of uniform density

Answer 1

Answer:

•At a point inside the solid sphere: V

inside

=

2R

3

−GM

(3R

2

−x

2

)

V

inside

=−GM(

2R

3

−

2R

3

r

2

); (if x=R)

At a point on the surface of the solid sphere:V

surface

=

R

−GM

; (If x=R)

At a point outside the solid sphere:V

outside

=

x

−GM

; (If x=R)

At the centre: x=0

⇒V

c

=−

2

3

R

GM

=

2

3

V

surface

in case of solid sphere potential is maximum at centre.

We have,

Gravitational potential on Earth =V

Now,

Gravitaional potential at the centre of the Earth =V

C

= 23V

s

surface =

23V

Explanation:

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