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  • Assuming the earth to be a sphere of uniform mass density, how much would a body weigh half way down to the centre of the earth if it weighed 250 N on the surface ?

Q: 8.16 Assuming the earth to be a sphere of uniform mass density, how much would a body weigh half way down to the centre of the earth if it weighed \small 250\hspace {1mm}N on the surface?

Answers (1)

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Position of the body is (depth)  :

                                                 =\ \frac{1}{2}R_e

Acceleration due to gravity at depth d is given by :

                                             g'\ =\ \left ( 1\ -\ \frac{d}{R_e} \right )g

or                                                =\ \left ( 1\ -\ \frac{\frac{R_e}{2}}{R_e} \right )g

or                                                =\ \frac{1}{2}g

Thus the weight of the body is:- 

                                            W\ =\ mg'

or                                                 =\ m\times \frac{1}{2}g\ =\ \frac{mg}{2}

or                                                 =\ 125\ N

Thus the weight of the body is 125 N.

Posted by

Devendra Khairwa

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