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A man weighs 'W' on the surface of the e...

A man weighs 'W' on the surface of the earth and his weight at a height 'R' from surface of the earth is (`R` is Radius of the earth )

Text Solution

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(i) (1) Here, the weight of the person on the surface of the Earth is 'w'. Then, w = mg
`= (GMm)/(R^(2))`
(2) Then, the weight of the person, (i.e.,) gravitational force of attraction on the person at a height 'h' will be,
`w_(h) = (GMm)/((R + h)^(2))`
Given that height is equal to 'R' Substitute, 'R' in place of 'h' in equation (2). Find the value of `'w_(h)'` in terms of 'w'.
(ii) `W_(h) = (W)/(4)`
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