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Q: 8.15  A body weighs 63\hspace {1mm}Non the surface of the earth. What is the gravitational force on it due to the earth at a height equal to half the radius of the earth?

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Acceleration due to gravity at height h from the surface of the eath is :

                                        g'\ =\ \frac {g}{\left ( 1\ +\ \frac{h}{R} \right )^2}

For     h\ =\ \frac{R}{2}    we have :

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

or                                                          =\ \frac{4}{9}g

Thus the weight of the body will be : 

                                                    W\ =\ mg'

or                                                         =\ m\times \frac{4}{9}g\ =\ \frac{4}{9}mg

or                                                          =\ 28\ N

Posted by

Devendra Khairwa

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