Question

Three blocks I, II & III having the mass of 1.6 kg, 1.6 kg and 3.2 kg respectively are connected as shown in the figure. The linear mass density of the wire AB, CD, and DE are 10 g/m, 8 g/m, and 10 g/m respectively. The speed of a transverse wave pulse produced in AB, CD, and DE are : ($g=10m/{sec}^2$)

• A. 80 m/s, 20 $\sqrt{1}0$ m/s, 40 m/s
• B. 20 $\sqrt{1}0$ m/s, 40 m/s, 80 m/s
• C. 20 $\sqrt{1}0$ m/s in all
• D. 80 m/s in all

Answer 1

The correct option is A 80 m/s, 20 $\sqrt{1}0$ m/s, 40 m/s

Tension in string AB

$T_{AB}=(m_1+m_2+m_3)g$

$=(1.6+1.6+3.2)\times 10$

$=64N$

Tension in string CD

$T_{CD}=(m_1+m_2)g$

$=(1.6+1.6)\times 10$

$=32N$

Tension in string DE

$T_{DE}=m_{1}g$

$=1.6\times 10$

$=16N$

Velocity of string AB = $V_{AB}=\sqrt{\frac{T_{AB}}{{\mu }_{AB}}}=\sqrt{\frac{64}{0.01}}=80m/s$

Velocity of string CD = $V_{CD}=\sqrt{\frac{T_{CD}}{{\mu }_{CD}}}=\sqrt{\frac{32}{0.008}}=20\sqrt{10}m/s$