Question

Value of gravitational acceleration at a depth equal to half of the radius of the earth will be:-(Take g=10m/sec^2 at the surface of the earth)

Answer 1

The answer to the question will be $5 m/s^2$

DERIVATION:

The value of acceleration due to gravity on the surface of earth is g.

As per the question, the value of g is given as $10\ m/s^2$

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

Let R is the radius of earth and the value of gravitational acceleration at depth equal to half of the radius of earth is g'.

The value of gravitational acceleration at a depth d is calculated as -

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

Here, d = $\frac{R}{2}$

Hence, the value of g' will be -

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

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

                                               $=g\times \frac{1}{2}$

                                               $=\frac{10\ m/s^2}{2}$

                                               $= 5\ m/s^2$      [ans]      

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.