Question

What will be the value of g at the bottom of sea 7 km deep? ( radius of earth = 6400 km and "g" on the surface of earth = 9.8 m/s2)?

Answer 1

as depth increase g linear ly decrease

Answer 2

Given:

• Radius of earth = 6400 km
• Value of 'g' at surface = 9.8 m/s²

To find:

• Value of gravitational acceleration 7 km at bottom of sea ?

Calculation:

The general expression of gravitational acceleration at depth D is :

$\boxed{ g_{D} = g \times( 1 - \dfrac{D}{r} )}$

• 'D' refers to depth below earth surface. 'r' refers to radius of earth.

• Putting necessary values in SI unit :

$\implies g_{D} = 9.8 \times( 1 - \dfrac{7}{6400} )$

$\implies g_{D} = 9.8 \times( 1 - 0.001 )$

$\implies g_{D} = 9.8 \times 0.999$

$\implies g_{D} = 9.79 \: m/ {s}^{2}$

So, value of gravitational acceleration at 7 km depth is 9.79 m/s².