The linear charge density of a thin rod of length L is given by λ=(λ0x)Coulomb/m,[0≤x<L2] and λ=(λ0x2)Coulomb/m,[L2≤x≤L]. Find the total charge on rod. (x is measure from one end of the rod).
A
λ0L224(3+7L)
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B
λ0L38(1+5L)
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C
λ0L24(1+7L)
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D
λ0L2(1+7L)
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Solution
The correct option is Aλ0L224(3+7L) Total charge on AB can be calculated by,
qAB=x=L2∫x=0λdx
From the data given in the question,
qAB=x=L2∫x=0λ0xdx
⇒qAB=λ0[x22]x=L2x=0
∴qAB=λ0L28
Similarly , total charge on BC can be calculated by,