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).
C
Acceleration due to gravity increases with increasing latitude.
D
Acceleration due to gravity is independent of the mass of the earth.

✓

Answer

Acceleration due to gravity decreases with increasing altitude.

Acceleration due to gravity increases with increasing latitude.

Explanation:

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

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), $\text{gd}=\text{g}\Big(1-\frac{\text{d}}{\text{R}}\Big).$

Increasing depth (d) decreases the value of ga . Option (b) is incorrect.

If $\lambda$ is latitude on earth then $\text{g}\lambda=\text{g}-\omega^2\text{R}\cos^2\lambda$

As value of cos decrease from 0°to 90° (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.

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