Q53 / 75 · JEE Main 2020 (08 Jan Shift 2) · Physics

A transverse wave travels on a taut steel wire with a velocity of $v$ when tension in it is $2.06 \times 10^{4} N .$ When the tension is changed to $T,$ the velocity changed to $\frac{v}{2} .$ The value of $T$ is close to:

A
$2.50 \times 10^{4} N$
Correct answer
B
$5.15 \times 10^{3} N$
C
$30.5 \times 10^{4} N$
D
$10.2 \times 10^{2} N$

Solution

v \propto \sqrt{T}

\Rightarrow \frac{v_{1}}{v_{2}} = \sqrt{\frac{T_{1}}{T_{2}}} \Rightarrow \frac{v}{(\frac{v}{2})} = \sqrt{\frac{2.06 \times 10^{4}}{T}}

\Rightarrow T = \frac{2.06 \times 10^{4}}{4} N = 0.515 \times 10^{4} N

Hence, the correct answer is option: 'B'.

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