Question

Three blocks I, II & III having a 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, $20\sqrt{10}m/s$, 40 m/s
• B. $20\sqrt{10}m/s$, 40 m/s, 80 m/s
• C. $20\sqrt{10}m/s$ in all
• D. 80 m/s in all

Answer 1

The correct option is A 80 m/s, $20\sqrt{10}m/s$, 40 m/s

Tension in the string AB,

$T_{AB}=(m_1+m_2+m_3)g{T}_{AB}=(1.6+1.6+3.2)\times 10T_{AB}=64N$

Tension in the string CD

$T_{CD}=(m_1+m_2)\times g{T}_{CD}=(1.6+1.6)\times 10T_{CD}=32N$

Tension in string DE

$T_{DE}=m_{1}g=16N$

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

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

Velocity in strong DE=$V_{DE}=\sqrt{\frac{T_{DE}}{{\mu }_{DE}}}=\sqrt{\frac{16}{0.01}}=40m/s$

Hence option (A) is correct