A ball at O is in equilibrium as it is attached with two strings AO and DO which are tied at A and D. AO=DO=a√5. The charges at A, B, C and D are +q, +Q, +2Q and -q respectively. The ball O is positively charged then
A
The ball O can not remain in equilibrium.
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B
If the charge at C is +Q, the ball will remain in equilibrium.
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C
The ball at O will remain in equilibrium.
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D
If the charges at A and D and charges at B and C are interchanged, the ball will remain in equilibrium.
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Solution
The correct options are C The ball at O will remain in equilibrium. D If the charges at A and D and charges at B and C are interchanged, the ball will remain in equilibrium. For ball O (positively charged) to be in equilibrium at the middle of BC. [q4πϵ0(a√5)2+q4πϵ0(a√5)2]cosθ+Q4πϵ0a2=2Q4πϵ0a2 2qcosθ5+Q=2Q⇒q=5√5Q2 If q=5√5Q2, ball will be in equilibrium even if the charges are interchanged. If the charge at C is +Q, then 2qcosθ5+Q=Q 2qcosθ5=0,q≠0,θ=90∘