JEE PYQ: Waves And Sound Question 18
Question 18 - 2020 (07 Jan Shift 1)
Speed of a transverse wave on a straight wire (mass 6.0 g, length 60 cm and area of cross-section 1.0 mm$^2$) is 90 ms$^{-1}$. If the Young’s modulus of wire is $16 \times 10^{11}$ Nm$^{-2}$, the extension of wire over its natural length is:
(1) 0.03 mm
(2) 0.02 mm
(3) 0.04 mm
(4) 0.01 mm
Show Answer
Answer: (1)
Solution
Given, $l = 60$ cm, $m = 6$ g, $A = 1$ mm$^2$, $v = 90$ m/s and $Y = 16 \times 10^{11}$ Nm$^{-2}$
Using, $v = \sqrt{\frac{T}{m}} \times l \Rightarrow T = \frac{mv^2}{l}$
Again from, $Y = \frac{\Delta L / L_0}{T/A}$
$\frac{\Delta L}{l} = \frac{Tl}{l(YA)} = \frac{mv^2}{l(YA)}$
$= \frac{6 \times 10^{-3} \times 90^2}{16 \times 10^{11} \times 10^{-6}} = 3 \times 10^{-4}$ m
$= 0.03$ mm
BETA
