Question

Suppose you are standing on a tall ladder. If your distance from the centre of the earth is 2R, what will be your weight?
Please solve this. If not at least give the explanation how to do it.

Answer 1

Given:

A person is standing on a tall ladder and his distance from the centre of the Earth is 2R , R is the radius of Earth.

To find:

Weight of the man at that Height

Calculation:

First let's consider the weight of man at surface of earth to be mg.

Now we need to calculate the new gravitational acceleration at that height ;

Height of man from Earth Surface

=> h = 2R - R = R

Let new gravitational acceleration be g2

$g2 = \dfrac{g}{ {(1 + \dfrac{h}{R}) }^{2} }$

$= > g2 = \dfrac{g}{ {(1 + \dfrac{ \cancel R}{ \cancel R}) }^{2} }$

$= > g2 = \dfrac{g}{ {(1 + 1)}^{2} }$

$= > g2 = \dfrac{g}{4}$

So weight of man at that height will be :

W2 = m × g/4 = mg/4 .

Answer 2

Given that:

• Distance from center of earth is 2R.
• Radius of earth is R and mass of person is m.

To Find:

• Weight of the person standing on the tall ladder.

Formula Used:

• Weight (F) = m(geff)

• geff = g/(1+h/R)^2

Solution:

Distance of man from center of earth is 2R.

So, Distance from surface of earth = 2R-R = R

So, geff = g/(1+R/R)^2

geff = g/(2)^2

geff = g/4....(1)

Now, Using the above formula, we have

Weight = mass*geff

W = m*(1)

W = m*g/4

W = mg/4 N

So, the weight of the person is mg/4 N.

Hope this helps