Question

Calculate the value of g at the depth of 1600km below the surface of earth the value of g on the surface of earth is 9.8m/sec²,R=6400km​

Answer 1

Answer:

$\displaystyle{\text{g}_d=7.35 \ \text{m/sec}^2 }$

Explanation:

Given :

Depth ( d ) = 1600 km

Value of g at surface = 9.8 m / sec

Radius ( R ) = 6400 km

We have to find value of g at depth :

We have formula :

$\displaystyle{\text{g}_d=\text{g}\left(1-\dfrac{\text{d}}{\text{R}}\right)}$

Putting values here :

$\displaystyle{\text{g}_d=9.8\left(1-\dfrac{1600}{6400}\right)}$

$\displaystyle{\text{g}_d=9.8\left(1-\dfrac{1}{4}\right)}$

$\displaystyle{\text{g}_d=9.8\left(1-0.25\right)}$

$\displaystyle{\text{g}_d=9.8\left(0.75\right)}$

$\displaystyle{\text{g}_d=7.35 \ \text{m/sec}^2 }$

Hence we get answer.

Answer 2

$\bold{\underline{\underline{Answer:}}}$

Value of g at the depth of 1600 km is 7.35 m/s²

$\bold{\underline{\underline{Step\:-\:by\:-\:step\:explaination:}}}$

Given :

• Depth (d) = 1600 km
• Value of g (on earth's surface) = 9.8 m/s²
• Radius of earth = 6400 km

To find :

• Value of g at the depth of 1600 km.

Solution :

Since we need to calculate the value of g below the surface of the earth, we will use the following formula.

But let's make some assumptions before we hit up the formula.

Let $\bold{g_1}$ be the value of g at the depth of 1600 km.

$\bold{\underline{\underline{Formula:}}}$

$\bold{\large{\sf{g_1=\:g\times{\dfrac{(R-d)}{R}}}}}$

We have the values of :-

$\rightarrow$ g = 9.8 m/s²

$\rightarrow$R = 6400 km

$\rightarrow$d = 1600 km

Block in the values in the formula,

$\rightarrow$ $\bold{g_1=\:9.8\:\times\:{\dfrac{(6400-1600)}{6400}}}$

$\rightarrow$ $\bold{g_1=9.8 \times\:{\dfrac{4800}{6400}}}$

$\rightarrow$ $\bold{g_1\:={\dfrac{47,040}{6400}}}$

$\rightarrow$ $\bold{g_1=\:7.35}$

$\bold{g_1=value\:of\:at\:depth\:of\:1600\:km\:=\:7.35\:mpersec^2}$