-->

Atoms And Molecules

Question
CBSEENSC9006145

If your weight is 60 kg on earth, how far must you go from the centre of the earth so that you weigh 30 kg?

Solution

Weight of a body varies inversely as the square of the distance from the centre of the earth.
Therefore,
      straight W subscript 2 over straight W subscript 1 space equals space fraction numerator straight R subscript 1 superscript 2 over denominator straight R subscript 2 superscript 2 end fraction 
rightwards double arrow 30 over 60 space equals space fraction numerator straight R subscript straight e superscript 2 over denominator straight R subscript 2 superscript 2 end fraction          (Re = Radius of the earth)
rightwards double arrow space space space space space 1 half space equals space fraction numerator straight R subscript straight e superscript 2 over denominator straight R subscript 2 superscript 2 end fraction space space space space
rightwards double arrow space space fraction numerator 1 over denominator square root of 2 end fraction space equals space straight R subscript straight e over straight R subscript 2
rightwards double arrow space space space space space space space space straight R subscript 2 space equals space square root of 2 straight R subscript straight e
B u t comma

R a d i u s space o f space t h e space E a r t h comma space straight R subscript straight e space equals space 6.4 space cross times space 10 to the power of 6 straight m

therefore space space space space space space space straight R subscript 2 space equals space 1.414 space cross times space 6.4 space cross times space 10 to the power of 6 straight m space
space space space space space space space space space space space space space space space space space equals space 9.05 space cross times space 10 to the power of 6 straight m

So, at a distance of 9.05 x 106m from the centre of the earth, 100 kg -wt will become 30 kg-wt.