Question

compression between the acceleration due to gravity'g' in ladakh and the value of digha west bengal?​

Answer 1

To compare:

The acceleration due to gravity'g' in ladakh and the value of digha west bengal?

Solution:

Let us consider that LADAKH is situated at a height h above earth surface, and DIGHA is situated at sea level (i.e. can be considered as earth surface).

At Digha, the gravitational acceleration will be:

$\therefore \: g_{(digha)} = \dfrac{GM}{ {R}^{2} } \: \: \: \: ......(1)$

At Ladakh, the gravitational acceleration will be:

$\therefore \: g_{(ladakh)} = \dfrac{GM}{ {(R + h)}^{2} } \: \: \: \: ......(2)$

Dividing the equations:

$\therefore \: \dfrac{ g_{(digha)}}{g_{(ladakh)}} = \dfrac{{(R + h)}^{2} }{ {R}^{2} }$

When h << R :

$\implies\: \dfrac{ g_{(digha)}}{g_{(ladakh)}} = {(1 + \dfrac{h}{R}) }^{2}$

Applying Binomial Approximation:

$\implies\: \dfrac{ g_{(digha)}}{g_{(ladakh)}} = 1 +2 (\dfrac{h}{R})$

$\boxed{ \bf\implies\: g_{(digha)} = g_{(ladakh)}\bigg \{ 1 +2 (\dfrac{h}{R}) \bigg \}}$