Question

Consider an object of mass 50 kg. Estimate the weight of the object at a distance R, 2R, 4R, 6R and 10R from the centre of the earth. Plot a graph showing the weight of the object with respect to the distance from the centre of the earth.

Answer 1

Consider an object of mass 50 kg. Estimate the weight of the object at a distance R, 2R, 4R, 6R and 10R from the centre of the earth. Plot a graph showing the weight of the object with respect to the distance from the centre of the earth

Answer 2

The weights are given below:

The mass of the object is = 50 kg

• The weight of the object at a distance R from the center of the Earth will be  = 50g N

                    = 500 N

The value of acceleration due to gravity at a height h from the surface of the Earth is,

g' = g (1+h/R)⁻²

For, small value of h, we can consider the equation as,

g' = g (1-2h/R)

• For, a height of 2R from the center of the Earth, the value of g will be,

                 g' = $\frac{g}{(1+\frac{2R}{R})^2 }$

[Distance from center is = 2R, so distance from earth surface will be = (2R -R) =R]

Or, g' = g/9

The weight of the object at a distance 2R from the center of the Earth will be = 500/9 N = 55.55 N

• The weight of the object at a distance 4R from the center of the Earth will be = 500/16 = 31.25 N
• The weight of the object at a distance 6R from the center of the Earth will be = 500/36 = 13.88 N
• The weight of the object at a distance 10R from the center of the Earth will be = 500/100 = 5 N

The graph is attached here:

Please find the attachment.

ab959253cb3c1da40f80df25f146299d.docx