Which of the following options are correct? - Vidyadip

MCQ

Which of the following options are correct?

A
Acceleration due to gravity decreases with increasing altitude.
B
Acceleration due to gravity increases with increasing depth $($assume the earth to be a sphere of uniform density$)$. and Acceleration due to gravity increases with increasing latitude.
✓
$A$ and $B$
D
Acceleration due to gravity is independent of the mass of the earth.

✓

Answer

Correct option: C.

$A$ and $B$

The acceleration due to gravity at an altitude $($height$), gh =g(1-2).$

As value of $\cos$ decrease from $0^\circ$ to $90^\circ ($from $1$ to $0).$ The acceleration due to gravity increases from equator $(\lambda=0^0)$ to pole $(\lambda=90^0).$ Option $(c)$ is correct.
The acceleration due to gravity on surface of earth is $\text{g}=\frac{\text{GM}_\in}{\text{R}^2_\in}$ So $g$ on earth depends on mass of earth. Option $(d)$ is incorrect.
Increasing depth $(d)$ decreases the value of ga . Option $(b)$ is incorrect.
If $\lambda$ is latitude on earth then $\text{g}\lambda=\text{g}-\omega^2\text{R}\cos^2\lambda$
Increasing height $(h)$ decreases the value of $gh$ option $(a)$ is correct.
Assuming the earth to be a sphere of uniform density, the acceleration due to gravity at a particular depth $(d), \text{gd}=\text{g}\Big(1-\frac{\text{d}}{\text{R}}\Big).$

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