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Home / Doubts and Solutions/JEE/Physics

Question 13

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Asked by hrittik12d 31st October 2018, 11:52 AM
Answered by Expert
Answer:
                         
two spheres are suspended from the silk thread whose mass
 
m = 10-6 kg 
the length of thread is AB = 50 cm =0.5 cm 
The two spheres are seperated by a distance AC = 20 cm =0.2 m 
from figure, AC = AD + DC 
Thus AD = 0.1 m 
 
By Pythagoras theorem,
AB2 = BD2 + AD2 
 
(0.5)2 = BD2 + 0.12 
 
BD2 = 0.52 - 0.12 
 
BD2 = (0.5 + 0.1) (0.5 - 0.1)
 
BD2 = 0.24
BD = 0.48
 
From figure we can observe,
 
fraction numerator F over denominator A D end fraction equals fraction numerator m g over denominator B D end fraction F equals fraction numerator m g cross times A D over denominator B D end fraction  
By Coulomb's law,
F equals fraction numerator 1 over denominator 4 pi epsilon subscript 0 end fraction space fraction numerator q squared over denominator A C squared end fraction fraction numerator 1 over denominator 4 pi epsilon subscript 0 end fraction equals 9 space x space 10 to the power of 9 space N. space m squared space divided by C squared rightwards double arrow space fraction numerator 1 over denominator 4 pi epsilon subscript 0 end fraction space fraction numerator q squared over denominator A C squared end fraction space equals space fraction numerator m g space cross times A D over denominator B D end fraction fraction numerator 9 space x space 10 to the power of 9 over denominator open parentheses 0.2 close parentheses squared end fraction space q squared equals space fraction numerator 10 to the power of negative 6 end exponent space cross times space 9.8 space cross times space 0.1 over denominator 0.48 end fraction S o l v i n g space w e space g e t comma q squared space equals space 9 space cross times 10 to the power of negative 18 space end exponent C squared rightwards double arrow space q space equals space 3 space cross times 10 to the power of negative 9 end exponent space C
Hence, the charge on each sphere is 3 × 10-9 Coulombs
Answered by Expert 31st October 2018, 4:24 PM
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