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GATE 2024 ME – Question 27

Engineering Mechanics · Free-body diagrams and equilibrium · 1 mark · Multiple choice

A rigid massless tetrahedron is placed such that vertex O is at the origin and the other three vertices A, B, and C lie on the coordinate axes as shown in the figure. The body is acted on by three point loads, of which one is acting at A along $x$-axis and another at point B along $y$-axis. For the body to be in equilibrium, the third point load acting at point O must be

A tetrahedron OABC with O at the origin and A, B and C on the $x$, $y$ and $z$ axes respectively.
  1. along $z$-axis
  2. in $x-y$ plane but not along $x$ or $y$ axis
  3. in $y-z$ plane but not along $y$ or $z$ axis
  4. in $z-x$ plane but not along $z$ or $x$ axis

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Show answer and explanation

Correct answer: (B) in $x-y$ plane but not along $x$ or $y$ axis

Explanation

A is on the $x$-axis, so the load at A along the $x$-axis acts along the line OA and passes through O. In the same way the load at B along the $y$-axis acts along OB and passes through O. The two forces meet at O and add up to a resultant at O that lies in the $x-y$ plane. The load at O has to cancel it, so it also lies in the $x-y$ plane, and in general it is not along the $x$ or the $y$ axis.