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8.Mechanical Properties of Solids
medium
The dimensions of four wires of the same material are given below. In which wire the increase in length will be maximum when the same tension is applied
A
Length $100 \,cm,$ Diameter $1 \,mm$
B
Length $200\, cm,$ Diameter $2\, mm$
C
Length $300$ $cm$, Diameter $3 \,mm$
D
Length $50$ $cm,$ Diameter $0.5$ $mm$
Solution
(d)$Y = \frac{F}{A}\;\frac{L}{A} \Rightarrow l \propto \frac{L}{A} \propto \frac{L}{{\pi {d^2}}}$
$l \propto \frac{L}{{{d^2}}}$ [As F and Y are constant]
The ratio of $\frac{L}{{{d^2}}}$is maximum for case $(d)$
Standard 11
Physics
