Question

find the height at which value of g at the point is equal to value of g at a depth of 600 km from the surface​

Answer 1

Answer:

Correct option is

C

7.35ms

−2

Given : d=1600km R=6400km

Acceleration due to gravity at a depth d, g

d

=g

s

(1−

R

d

)

where g

s

=9.8ms

−2

is acceleration due to gravity at earth's surface.

∴ g

d

=9.8(1−

6400

1600

)=7.35ms

−2

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Answer 2

Concept:

• Gravitational Force
• Acceleration due to gravity

Given:

• Depth from surface d = 600km = 600000m
• Radius R = 6400km = 6400000m

Find:

• Height at which value of g at the point is equal to the value of g at a depth of 600 km from the surface

Solution:

Acceleration due to gravity g at depth d = g(1-d/R)

Acceleration due to gravity g at height h = g (1-2h/R)

The acceleration due to gravity in both cases has to be the same.

g (1-2h/R) = g(1-d/R)

1-2h/R = 1-d/R

2h/R = d/R

2h= d

h=d/2

h= 600km/2

h= 300km

At a height of 300km above the surface, the value of g will be the same as that of 600km below the surface.

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