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Sanchit Gupta Grade: 12
        

Find the force on a particle of mass m placed at the centre of a semicircular wire of length L and mass M.

7 years ago

Answers : (1)

Puneet Mittal AskiitiansExpert-IITD
22 Points
										


Hi Sanchit,


The answer is :


let R be raidus of wire , then , ∏R = L --- (1)


element of length RdΦ at angle Φ from centre will exert a force dF = Gm(M/L)(RdΦ)/R2


Similar force will be exerted by a element at angle -Φ from the centre.


Thus net force on m will be : 2dFcosΦ


Thus Force F = ∫2dFcosΦ   where Φ varies from 0 to 90


Thus F = 2∫(Gm(M/L)dΦ/R)cosΦ


F = 2GmM/LR ∫cosΦ dΦ where Φ varies from 0 to 90


F = 2GmM/LR ( 1 - 0 )


 Thus force on particle due to wire will be F = 2GMm/LR = 2GMm∏/L2 ( from (1) )


Please feel free to ask as many questions you have.


Puneet

6 years ago
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