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GATE 2020 ME (ME1) – Question 39

Engineering Mechanics · Impulse and momentum, energy formulations · 2 marks · Multiple choice

A 2 kg block rests on a smooth horizontal surface (top view) and is attached to a massless elastic cord of stiffness 5 N/m, hinged at O. The cord is initially unstretched at length 0.5 m and remains elastic. The block is given speed 1.5 m/s perpendicular to the cord. Find its speed when the cord has stretched by 0.4 m (m/s).

Diagram for GATE 2020 ME (ME1) question 39
  1. 0.83
  2. 1.07
  3. 1.36
  4. 1.50

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Show answer and explanation

Correct answer: (C) 1.36

Explanation

Conservation of mechanical energy gives $mv_0^2/2=mv^2/2+kx^2/2$. Thus $v=\sqrt{1.5^2-(5/2)(0.4)^2}=\sqrt{1.85}=\mathbf{1.36}$ m/s, **C**. The initial cord length does not enter its elastic energy, which depends on extension.