Help please ..... How far of a small sphere of 100 kg a particle would have to be placed so that the ball would attract the particle with the same force as the Earth? This experiment could be done effectively? How come?

Question

help!!!! · Answer

How far from the earth?

anonymous · Answer

the distance the question does not specify

abhisar · Answer

Mass of particle ?

fifciol · Answer

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$$\frac{ Gm_p m_s}{r_1^2 }=\frac{ GM_e m_s}{r_2^2 } \Rightarrow r_2 =r_1\sqrt{\frac{ M_e }{m_s }}$$

fifciol · Answer

the distance from particle to the Earth is sqrt Me/ms larger than the distance from particle to sphere, with these givens I'm not sure there could be more accurate solution

mrnood · Answer

I think you have misinterpreted the question.

My interpretation is 

Take the weight of the particle on earth 
What distance would a 100kg mass have to be to exert the same force (in the ABSENCE of other forces)

Weight = GMeM1/re^2     (re = radius of earth)

Force = G 100 M1/d^2     (d = distance from mass to particle)

d^2/re^2 = G100M1/GMeM1

=100/Me

SO d^2 = 100 re^2/Me
d= re * sqrt (100/Me)

mrnood · Answer

A quick estimate - I make this approx. 1x10-4m

= 0.1mm

You could not get a point mass of 100kg so small....

anonymous · Answer

I agree with MrNood

anonymous · Answer

correct????

mrnood · Answer

Are you saying this is the solution? 

It looks about right to me, and corresponds with the statement that oyu cannot get a point mass of sufficient denity.