Question 235: Gravitation

Question

The change in the value of $$g$$ at a height $$h$$ above the surface of the earth is the same as at a depth $$d$$ below the surface of earth. When both $$d$$ and $$h$$ are much smaller than the radius of earth, then which one of the following is correct?

Accepted Answer

At height h acceleration due to gravity, $${g_h} = g\left[ {1 - {{2h} \over R}} ight];$$
At depth d acceleration due to gravity, $${g_d} = g\left[ {1 - {d \over R}} ight]$$
According to the question,
$${g_h} = {g_d}$$
$$	herefore$$ $$g\left[ {1 - {{2h} \over R}} ight]$$ = $$g\left[ {1 - {d \over R}} ight]$$
$$ \Rightarrow {{2hg} \over R} = {{dg} \over R}$$
$$ \Rightarrow $$ $$d=2h$$

Answer

$$d = {{3h} \over 2}$$

Answer

$$d = {h \over 2}$$

Answer

$$d = h$$

Answer

$$d = 2\,h$$

Gravitation

The change in the value of $g at a height h above the surface of the earth is the same as at a depth d below the surface of earth. When both d and h$ are much smaller than the radius of earth, then which one of the following is correct?

Choose the correct answer: