Question

Value of gravitational acceleration at a depth equal to half of the radius of the earth

Answer 1

Let us consider the gravitational acceleration on the surface of earth is denoted as g.

The value of g on the surface of earth = $9.8\ m/s^2$

We are asked to calculate the acceleration due to gravity at a depth equal to half of the radius of earth.

The acceleration due to gravity at a depth d is calculated as -

                                          $g'\ = g(1-\frac{d}{R})$

Here, R is the radius of earth and d is the depth.

 Here, d = $\frac{R}{2}$

Hence, the gravitational acceleration $g'\ =\ g(1-\frac{R/2}{R})$

                                                                     $=\ g(1-\frac{1}{2})$

                                                                     $=\ \frac{g}{2}$

                                                                     $=\frac{9.8}{2}\ m/s^2$

                                                                     $=\ 4.9\ m/s^2$

Hence, the acceleration due to gravity at depth equal to half of radius is $4.9\ m/s^2$

Answer 2

Gravitational acceleration: The acceleration acted on an object that is caused caused by the force of gravitation is called as gravitational acceleration.

It is used to indicate the intensity of a gravitational field.

Given:

g = 10 m/sec^2  

To find:

The value of gravitational acceleration at a depth equal to half of the radius of the earth.

Solution:

Consider r to be the radius of the earth.

Then,

Gravitational acceleration at depth d,

g' = g ( 1 - d/r )

In this context,

The depth equal to half of the radius,

d = r/2

Hence,

g' = g ( 1 - r/2/r)

g' = g * 1/2

That is,

g' = 10 * 1/2

g' = 5 m/sec^2

Hence, The value of gravitational acceleration at a depth equal to half of the radius of the earth is 5 m/sec^2.

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