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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 2 kg block is suspended from the ceiling using a massless spring...

A 2 kg2 \text{ kg} block is suspended from the ceiling using a massless spring having a spring constant k=100 N/mk = 100 \text{ N/m}. Find the elongation of the spring. If an additional 1 kg1 \text{ kg} is attached to the block, what would be the further elongation?

Options

  1. A0.1 m0.1 \text{ m} and 0.2 m0.2 \text{ m}
  2. B0.2 m0.2 \text{ m} and 0.1 m0.1 \text{ m}
  3. C0.2 m0.2 \text{ m} and 0.3 m0.3 \text{ m}
  4. D0.3 m0.3 \text{ m} and 0.1 m0.1 \text{ m}

Correct answer

B. 0.2 m0.2 \text{ m} and 0.1 m0.1 \text{ m}

Step-by-step solution

Given m1=2 kgm_1 = 2 \text{ kg}, k=100 N/mk = 100 \text{ N/m}, and taking g=10 m/s2g = 10 \text{ m/s}^2.

At equilibrium, the restoring force of the spring balances the weight of the block.

kx1=m1gk x_1 = m_1 g

100x1=2×10100 x_1 = 2 \times 10

x1=0.2 mx_1 = 0.2 \text{ m}

When an additional mass m2=1 kgm_2 = 1 \text{ kg} is attached, the additional restoring force balances the additional weight.

kx2=m2gk x_2 = m_2 g

100x2=1×10100 x_2 = 1 \times 10

x2=0.1 mx_2 = 0.1 \text{ m}

The initial elongation is 0.2 m0.2 \text{ m} and the further elongation is 0.1 m0.1 \text{ m}.
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