Question

Match Column - I with Column - II and mark the correct option from the codes given below

Answer 1

The acceleration due to gravity $g$ is never constant. In fact it is also not same everywhere on Earth's surface. It is maximum at poles and minimum at equator. However it is usually taken to be $9.8m/s^2$ because the variation is very little. But for calculating value of $g$ at height or depth, following expressions are used:

For a height $h$ above the earth's surface.
If $h<<R$ then acceleration due to gravity $g^{\prime }=g(1-2h/R)$
For depth $h$ below the earth's surface, acceleration due to gravity $g^{\prime }=g(1-h/R)$
If the Earth were a non-rotating perfect sphere, the acceleration due to gravity would be constant. Because of rotation, the Earth is flattened at poles. $G$ at the poles is greater than $G$ at the equator because $R$ at the poles is less than $R$ at the equator.
The gravitational force due to M is $\frac{GM}{R^2}$.
The right matches are given below.
$A\to 1$,
$B\to 3$,
$A\to 4$,
$D\to 2$.