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A body of weight 80 kg is taken inside the surface of earth. At what depth its weight will be 60 kg (assuming density of earth to be uniform )

A body of weight 80 kg is taken inside the surface of earth. At what depth its weight will be 60 kg  (assuming density of earth to be uniform ) 

Grade:11

2 Answers

Arun
25750 Points
5 years ago
Dear student
 
I am getting my answer as 6400 km.
 
Please let me know, if this is correct tyen I will share my procedure.
 
 
Regards
Arun (askIITiana forum expert)
Agrata Singh
208 Points
5 years ago
If the weight of man on earth surface is,80 , assuming g on surface to be 10 his mass would be 80/10=8kg
For his weight to become 60 we need a different value of g as mass is constant
New value of g should be 60/8=7.5
Now the gravity at a depth d can be found from this formula:
g’=g(1-d/R)
Putting in the known values
7.5=10(1-d/R)
(1-d/R)=0.75
d/R=0.25
d=0.25R= R/4=1600km
(where R is radius of earth and =6400km

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