Question

Consider the following statements about acceleration due to gravity on earth and mark the correct statement(s) :

• A. The value of $g$ is constant throughout
• B. $g^{\prime }=g(1-\frac{d}{r})$
• C. $g$ is slightly less (by about $1$%) when distance $<200m$
• D. $g$ is slightly greater when distance $<200m$

Answer 1

Answer: (B)

$g^{\prime }=g(1-\frac{d}{r})$

Acceleration due to gravity at depth d, $g^{\prime }=g(1-\frac{d}{r})$, where $r$ is the radius of earth.

Thus $g$ is not constant throughout.

Also for $d=200m$ $g^{\prime }=g(1-\frac{200}{6400\times 1000})$

Now $\frac{g-g^{\prime }}{g}\times 100=.003$ %

Thus $g$ is much more less than $1$%.