Question

find the acceleration due to gravity at a depth of 3200 km from the earth's surface assuming that erth has uniform density ​

Answer 1

Answer:

• Acceleration due to gravity (g) at 3200 km is 5 m/s².

Given:

1. Depth (d) = 3200 Km
2. Radius of Earth (R) = 6400 Km

Explanation:

$\rule{300}{1.5}$

From the Formula. We know,

$\bigstar \; \large{\boxed{\tt g_h = g\left[1 - \dfrac{d}{R}\right]}}$

$\bold{Here}\begin{cases}\text{d Denotes Depth} \\ \text{R Denotes Radius of earth}\\ \text{g Denotes acceleration due to gravity}\end{cases}$

Now,

$\large{\boxed{\tt g_h = g\left[1 - \dfrac{d}{R}\right]}}$

Substituting the values,

$\longmapsto\large{\tt g_h = g\left[1 - \dfrac{3200}{6400}\right]}$

$\longmapsto\large{\tt g_h = g\left[1 - \cancel{\dfrac{3200}{6400}}\right]}$

$\longmapsto\large{\tt g_h = g\left[1 - \dfrac{1}{2}\right]}$

$\longmapsto\large{\tt g_h = g\left[\dfrac{2 - 1}{2}\right]}$

$\longmapsto\large{\tt g_h = g\left[\dfrac{1}{2}\right]}$

∵ Acceleration Due to gravity (g) at earth is 10 m/s².

Substituting,

$\longmapsto\large{\tt g_h = 10 \times \left[\dfrac{1}{2}\right]}$

$\longmapsto\large{\tt g_h = \left[\dfrac{10}{2}\right]}$

$\longmapsto\large{\tt g_h = \left[\cancel{\dfrac{10}{2}}\right]}$

$\longmapsto\large{\underline{\boxed{\red{\tt g_h = 5 \; m/s^2}}}}$

∴ Acceleration due to gravity (g) at 3200 km is 5 m/s².

$\rule{300}{1.5}$