IF the diameter of the cross section of a wire is decreased by 5% how much% will the length be increased so that its volume remains same
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wire shape just like cylinder
hence
volume of cylindrical wire (v)=pi.r^2.L
let length of wire(L)=100 unit
radius of wire =100 unit
now volume of wire =pi. (100)^2.100
=10^6 pi cube unit
now radius decreases 5%
hence new radius of wire =100-5=95 unit
length of wire =?
volume of wire =10^6pi cube unit
10^6 pi.=pi. (95)^2.L'
L=110.8 unit
but we know initial length of wire =100
hence increment =10.8 unit
hence % increment =10.8/100 x 100=10.8 %
hence
volume of cylindrical wire (v)=pi.r^2.L
let length of wire(L)=100 unit
radius of wire =100 unit
now volume of wire =pi. (100)^2.100
=10^6 pi cube unit
now radius decreases 5%
hence new radius of wire =100-5=95 unit
length of wire =?
volume of wire =10^6pi cube unit
10^6 pi.=pi. (95)^2.L'
L=110.8 unit
but we know initial length of wire =100
hence increment =10.8 unit
hence % increment =10.8/100 x 100=10.8 %
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