Ncert Exercises & Solutions

The following are the given statements:

(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.

Choose the correct alternatives:

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.