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ICSE Class 9 Answered

a man weighs 600N at the earth surface.At what height above the surface of earth will he weigh 300N.(take radius of earth to be 6400km).  
Asked by dishaprep | 01 Sep, 2018, 10:56: PM
answered-by-expert Expert Answer
Let m be mass of man. Let g and g' are acceleration due to gravity on earth's surface
and at a height above earth's surface respectively

Weight of man on earth's surface = m×g = 600 N ...............(1)
Weight of man at a height above earth's surface = m×g' = 300 N .............(2)
 
from (1) and (2), we get begin mathsize 12px style fraction numerator g over denominator g apostrophe end fraction space equals space fraction numerator begin display style bevelled fraction numerator G M over denominator R squared end fraction end style over denominator begin display style bevelled fraction numerator G M over denominator begin display style open parentheses R plus h close parentheses squared end style end fraction end style end fraction space equals space fraction numerator begin display style open parentheses R plus h close parentheses squared end style over denominator R squared end fraction space equals space 2 space.............. left parenthesis 3 right parenthesis end style
G is gravitational constant, M is mass of earth and R is radius of earth.

By solving eqn.(3) for h, we get begin mathsize 12px style h space equals space fraction numerator R over denominator open parentheses 1 plus square root of 2 close parentheses end fraction equals fraction numerator 6400 over denominator open parentheses 1 plus square root of 2 close parentheses end fraction equals 2651 space k m end style
Answered by Thiyagarajan K | 02 Sep, 2018, 06:32: AM

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