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?
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Answer 1

Answer:

We know formula of Acceleration due to gravity at h height from the Earth's surface is given by g = g₀/(1 + h/R)²

Here, g₀ is the acceleration due to gravity on Earth's surface.

h is the height from the Earth's surface.

R is the radius of earth .

A/C to question,

My distance from the centre of earth is 2R

So, my distance from the surface of earth is 2R - R = R

∴ g = g₀/( 1 + 1/1)² = g₀/(2)² = g₀/4

Hence, acceleration will be 1/4th times of acceleration at Earth's surface.

Hence , weight of body at 2R distance from centre of earth will be 1/4th of weight of body at Earth's surface.

hope it hepls you

Answer 2

$\quad\bf{ \pink{Question}}➭$

Suppose you are standing on a tall ladder. If your distance from the centre of the earth is 2R, what will be your weight?

$\quad\bf{ \pink{Answer}}➭$

$Weight, W = \frac{ GMm}{ {r}^{2} } = \frac{GMm}{(2R) ^{2}} = \frac{GMm}{4R ^{2}} \\ \\ = \frac{1}{4} (\frac{GMm}{R ^{2}}) \\ \\ = \frac{Weight \: on \: the \: surface \: of \: the \: earth \: }{4}$

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