A wire is loaded by $6\, kg$ at its one end, the increase in length is $12\, mm.$ If the radius of the wire is doubled and all other magnitudes are unchanged, then increase in length will be ......... $mm$
A$6$
B$3$
C$24$
D$48$
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B$3$
b (b) $l \propto \frac{1}{{{r^2}}}$.
If radius of the wire is doubled then increment in length will become $\frac{1}{4}$ times i.e. $\frac{{12}}{4} = 3mm$
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