JEE PYQ: Properties Of Matter Question 9
Question 9 - 2020 (09 Jan 2020 Shift 2)
Two steel wires having same length are suspended from a ceiling under the same load. If the ratio of their energy stored per unit volume is 1 : 4, the ratio of their diameters is:
(1) $\sqrt{2} : 1$
(2) $1 : 2$
(3) $2 : 1$
(4) $1 : \sqrt{2}$
Show Answer
Answer: (1)
Solution
Energy density $= \frac{1}{2} \frac{F^2}{A^2 Y} \propto \frac{1}{d^4}$
$\frac{u_1}{u_2} = \left(\frac{d_2}{d_1}\right)^4 \Rightarrow \frac{1}{4} = \left(\frac{d_2}{d_1}\right)^4 \Rightarrow \frac{d_1}{d_2} = \sqrt{2} : 1$
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