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GATE 2017 ME (ME1) – Question 24

Engineering Mechanics · Kinematics and dynamics of rigid bodies in plane motion · 1 mark · Multiple choice

A unit-mass particle moves in a plane with polar coordinates $r(t)=t^2$, $\theta(t)=t$. Find its kinetic energy at $t=2$.

  1. 4
  2. 12
  3. 16
  4. 24

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Correct answer: (C) 16

Explanation

In polar coordinates, $v^2=\dot r^2+(r\dot\theta)^2$. At $t=2$, $r=4$, $\dot r=2t=4$ and $\dot\theta=1$, so $v^2=4^2+4^2=32$. With unit mass, $T=mv^2/2=16$. This is C; the angular term is a tangential speed $r\dot\theta$, not simply $\dot\theta$.

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