Question 12: Gravitation

Question

What will be the acceleration due to gravity at a depth d, where g is acceleration due to gravity on the surface of earth?

Accepted Answer

Acceleration due to gravity at the surface of earth,
$$g = {{GM} \over {{R^2}}} = {4 \over 3}\pi \rho GR$$ ...... (i)
[$$\because$$ $$M = {4 \over 3}\pi {R^3}\,.\rho $$]
Where, $$\rho$$ = density of earth.
Acceleration due to gravity at depth d from the surface of earth,
$$g' = {4 \over 3}\pi \rho G(R - d)$$ ...... (ii)
From Eqs. (i) and (ii), we get,
$$g' = g\left[ {1 - {d \over R}} \right]$$

Answer

$${g \over {{{\left[ {1 + {d \over R}} \right]}^2}}}$$

Answer

$$g\left[ {1 - {{2d} \over R}} \right]$$

Answer

$${g \over {{{\left[ {1 - {d \over R}} \right]}^2}}}$$

Answer

$$g\left[ {1 - {d \over R}} \right]$$

Gravitation

What will be the acceleration due to gravity at a depth d, where g is acceleration due to gravity on the surface of earth?

Choose the correct answer: