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

(C) $5.15 \times 10^{3} \mathrm{~N}$

(A) $10.2 \times 10^{2} \mathrm{~N}$

(B) $30.5 \times 10^{4} \mathrm{~N}$

(D) $2.50 \times 10^{4} \mathrm{~N}$

JEE Main · 2020 · 08 Jan 2020 · Shift 2 · Waves & Sound

A transverse wave travels on a taut steel wire with a velocity of v when tension in it is

2.06 \times 1 0^{4} N

. When the tension is changed to T, the velocity changed to

v /2

. The value of T is close to:

Answer: (C)

The speed of a transverse wave on a wire goes as

v \propto T

, so

\frac{v _{1}}{v _{2}} = \frac{T _{1}}{T _{2}}

. Halving the speed means

\frac{v}{v /2} = 2 = \frac{2.06 \times 1 0 ^{4}}{T}

, so

\frac{2.06 \times 1 0 ^{4}}{T} = 4

and

T = \frac{2.06 \times 1 0 ^{4}}{4} \approx 5.15 \times 1 0^{3}

JEE Main · 2020 · 08 Jan 2020 · Shift 2 · Single correct option