If the change in the value of g at a height h above the surface of the earth is the same as at a depth x below its surface, then:

Question

If the change in the value of g at a height h above the surface of the earth is the same as at a depth x below its surface, then: (A) x=h2 (B) x=0.5 h (C) x=2 h (D) x=h

Tardigrade Admin · Accepted Answer

The value of g decreases on going above and below the earth's surface. The value of g at a height h above the earth's surface of radius R is given by g'=g(1-(Z h/R)) ...(1) The value of g at a depth x below the surface of earth is given by g''=g(1-(x/R)) ...(2) Given, g'=g'' ∴ g(1-(2 h/R))=g(1-(x/R)) ⇒ x=2 h

Q. If the change in the value of $g$ at a height $h$ above the surface of the earth is the same as at a depth $x$ below its surface, then:

$x = h^{2}$

$x = 0.5 h$

$x = 2 h$

$x = h$

Q. If the change in the value of g at a height h above the surface of the earth is the same as at a depth x below its surface, then:

x=h2

x=0.5h

x=2h

x=h

Q. If the change in the value of $g$ at a height $h$ above the surface of the earth is the same as at a depth $x$ below its surface, then:

$x = h^{2}$

$x = 0.5 h$

$x = 2 h$

$x = h$