Ncert Exercises & Solutions

Consider the following statements:

(a)	The acceleration due to gravity decreases with increasing altitude.
(b)	The acceleration due to gravity increases with increasing depth (assuming the Earth is of uniform density).
(c)	The acceleration due to gravity increases with increasing latitude.
(d)	The acceleration due to gravity is independent of the Earth's mass.

Choose the correct option from the given ones:

1.	(b), (d)	2.	(a), (c)
3.	(c), (d)	4.	(a), (c), (d)

Hint: Use the concept of factors affecting the acceleration due to gravity.

Step 1:Find the effect of height and depth on the acceleration due to gravity.

Acceleration due to gravity at altitude h,

g_{h} = \frac{g}{{(1 + h / R)}^{2}} ≃ g (1 - \frac{2 h}{R})

At depth d,

g_{d} = g (1 - \frac{d}{R})

In both cases with an increase in h and d, g decreases.

Explanation:

Step 2: Find the effect of latitude on the acceleration due to gravity.

At latitude

ϕ g_{ϕ} = g - ω^{2} R \cos^{2} ϕ

ϕ

increases,

g_{ϕ}

increases.

Also, we can conclude from the formulae, that it is independent of the mass of the Earth.