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Concepts Of Physics MCQ Edition [Volume 1]
Exam
Concepts Of Physics MCQ Edition [Volume 1]
Subject
Physics
Chapter
Wave Motion and Waves on a String

Concepts Of Physics MCQ Edition [Volume 1] · Physics · Wave Motion and Waves on a String

As shown in the figure, two blocks, each with a mass of 3.2 kg ,...

As shown in the figure, two blocks, each with a mass of 3.2 kg3.2 \text{ kg}, are connected by a wire CDCD. The entire system is suspended from the ceiling using another wire ABAB. The linear mass density of wire ABAB is 10 g m−110 \text{ g m}^{-1}, while that of wire CDCD is 8 g m−18 \text{ g m}^{-1}. Determine the speed of a transverse wave pulse produced in ABAB and in CDCD.
As shown in the figure, two blocks, each with a mass of 3.2 kg , are connected by a wire CD . The entire system is

Options

  1. A56 m s−156 \text{ m s}^{-1} and 63 m s−163 \text{ m s}^{-1}
  2. B79 m s−179 \text{ m s}^{-1} and 63 m s−163 \text{ m s}^{-1}
  3. C79 m s−179 \text{ m s}^{-1} and 89 m s−189 \text{ m s}^{-1}
  4. D63 m s−163 \text{ m s}^{-1} and 79 m s−179 \text{ m s}^{-1}

Correct answer

B. 79 m s−179 \text{ m s}^{-1} and 63 m s−163 \text{ m s}^{-1}

Step-by-step solution

Given:
Mass of each block, m=3.2 kgm = 3.2 \text{ kg}
Linear mass density of wire ABAB, μAB=10 g m−1=0.01 kg m−1\mu_{AB} = 10 \text{ g m}^{-1} = 0.01 \text{ kg m}^{-1}
Linear mass density of wire CDCD, μCD=8 g m−1=0.008 kg m−1\mu_{CD} = 8 \text{ g m}^{-1} = 0.008 \text{ kg m}^{-1}
Acceleration due to gravity, g=9.8 m s−2g = 9.8 \text{ m s}^{-2}

The tension in wire CDCD is provided by the weight of the lower block:
TCD=mg=3.2×9.8=31.36 NT_{CD} = mg = 3.2 \times 9.8 = 31.36 \text{ N}

The speed of the transverse wave pulse in CDCD is:
vCD=TCDμCD=31.360.008=3920≈62.6 m s−1≈63 m s−1v_{CD} = \sqrt{\dfrac{T_{CD}}{\mu_{CD}}} = \sqrt{\dfrac{31.36}{0.008}} = \sqrt{3920} \approx 62.6 \text{ m s}^{-1} \approx 63 \text{ m s}^{-1}

The tension in wire ABAB is provided by the weight of both blocks (neglecting the mass of the wires):
TAB=2mg=2×3.2×9.8=62.72 NT_{AB} = 2mg = 2 \times 3.2 \times 9.8 = 62.72 \text{ N}

The speed of the transverse wave pulse in ABAB is:
vAB=TABμAB=62.720.01=6272≈79.2 m s−1≈79 m s−1v_{AB} = \sqrt{\dfrac{T_{AB}}{\mu_{AB}}} = \sqrt{\dfrac{62.72}{0.01}} = \sqrt{6272} \approx 79.2 \text{ m s}^{-1} \approx 79 \text{ m s}^{-1}

Thus, the speeds in ABAB and CDCD are 79 m s−179 \text{ m s}^{-1} and 63 m s−163 \text{ m s}^{-1} respectively.
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