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I hope the image will be clear to you. Please answer the question.

I hope the image will be clear to you. Please answer the question.

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Grade:12th pass

2 Answers

Parth
58 Points
3 years ago
See in this case F = GMm/(r^2)
for a cavity, you can assume a complete earth wit a -ve mass of same as cavity at the position of the cavity
So mass of cavity = rho*(4/3)*pi*(r/2)^3 , = -M/8, M= mass of earth
given that cavity touches particle
so Now Net force = GMm/(r^2) – G*(M/8)*m/(r/2)^2 =  GMm/(2*r^2)
so option A = F/2
pls approve if it helps
 
Ayush_Deep
120 Points
3 years ago
The density of removed sphere as well as complete sphere is same as material is same .
Now mass of sphere is directly proportional to volume .
Volume of removed sphere is 1/8 times of complete sphere.
Let mass of complete sphere be 8M.
Then the mass of the removed sphere will be M ( rdius R/2)
Mass of remaining sphere is 7M
Now force due to complete sphere is F=G*8M*m/R²= 8GMm/R²
Force due to part of sphere which is removed is G*M*m/(R/2)²
          = 4 GMm/R² =F/2
Force due to remaing part will be F-F/2 = = =F/2.(option A)
Hope you understood well please approve.

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