A transverse wave travels on a taut steel wire with a velocity of v when tension in it is 2.06 × 10 ^ 4 N . When the tension is changed to T, the velocity changed to (v)/(2) . The value of T is close to:

Correct answer: B. 5.15 × 10 ^ 3 N v ∝ T ⇒ v _ 1 v _ 2 = T _ 1 T _ 2 ⇒ (v)/(((v)/(2))) = 2.06 × 10 ^ 4 T ⇒ T = 2.06 × 10 ^ 4 4 N = 0.515 × 10 ^ 4 N

JEE Main 20208 JanuaryEvening Shift

JEE Main 2020 · 8 January · Evening Shift · Physics · Waves and Sound

A transverse wave travels on a taut steel wire with a velocity of v...

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

\dfrac{v}{2} .

The value of

T

is close to:

B. $5.15 \times {10}^{3}N$

v ∝ \sqrt{T}

⇒ \dfrac{{v}_{1}}{{v}_{2}} = \sqrt{\dfrac{{T}_{1}}{{T}_{2}}} ⇒ \dfrac{v}{\left(\dfrac{v}{2}\right)} = \sqrt{\dfrac{2.06 \times {10}^{4}}{T}}

⇒ T = \dfrac{2.06 \times {10}^{4}}{4}N = 0.515 \times {10}^{4}N