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Concepts Of Physics MCQ Edition [Volume 1]
Exam
Concepts Of Physics MCQ Edition [Volume 1]
Subject
Physics
Chapter
Newton's Laws of Motion

Concepts Of Physics MCQ Edition [Volume 1] · Physics · Newton's Laws of Motion

A block of mass 0.2 kg is suspended from the ceiling by a light...

A block of mass 0.2 kg0.2 \text{ kg} is suspended from the ceiling by a light string. A second block of mass 0.3 kg0.3 \text{ kg} is suspended from the first block through another string. Determine the tensions in the upper and lower strings, respectively. Take g=10 m/s2g = 10 \text{ m/s}^2.

Options

  1. A5 N5 \text{ N} and 2 N2 \text{ N}
  2. B2 N2 \text{ N} and 3 N3 \text{ N}
  3. C5 N5 \text{ N} and 3 N3 \text{ N}
  4. D3 N3 \text{ N} and 5 N5 \text{ N}

Correct answer

C. 5 N5 \text{ N} and 3 N3 \text{ N}

Step-by-step solution

Let m1=0.2 kgm_1 = 0.2 \text{ kg} be the mass of the upper block and m2=0.3 kgm_2 = 0.3 \text{ kg} be the mass of the lower block.

For the lower block, the forces acting on it are its weight downwards and the tension T2T_2 of the lower string upwards. Since the system is in equilibrium:

T2=m2gT_2 = m_2 g

T2=0.3×10=3 NT_2 = 0.3 \times 10 = 3 \text{ N}

For the upper block, the forces acting on it are its weight downwards, the tension T2T_2 downwards, and the tension T1T_1 of the upper string upwards. Since it is in equilibrium:

T1=m1g+T2T_1 = m_1 g + T_2

T1=0.2×10+3=2+3=5 NT_1 = 0.2 \times 10 + 3 = 2 + 3 = 5 \text{ N}

Alternatively, the upper string supports the total mass of both blocks. Thus, the tension in the upper string is:

T1=(m1+m2)g=(0.2+0.3)×10=5 NT_1 = (m_1 + m_2)g = (0.2 + 0.3) \times 10 = 5 \text{ N}

The tensions in the upper and lower strings are 5 N5 \text{ N} and 3 N3 \text{ N}, respectively.
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