GATE 2026 PH – Question 65

Classical Mechanics · rigid body dynamics: inertia tensor, orthogonal transformations, Euler angles, torque free motion of a symmetric top · 2 marks · Numerical answer

A 15 cm long scale is held horizontally with one of its ends on the edge of a 1 m high table and the other end resting on one’s index finger. As the finger is removed (see figure below), the scale starts rotating about its end on the table. After 0.1 s, during which it has rotated by a negligibly small angle but has gained a rotational speed as it leaves the table and falls vertically towards the ground. When its centre of mass has fallen by 0.5 m, it has rotated by an angle θ. The value of θ in degrees (rounded off to one decimal place) is _____ (g = 9.8 m.s−2)

A 15 cm horizontal ruler extends over the edge of a 1 m high table.

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Correct answer: 179.0 to 180.0

Explanation

The initial angular acceleration about the edge is $\alpha=(mgL/2)/(mL^2/3)=3g/(2L)=98\ \mathrm{rad\,s^{-2}}$. After 0.1 s, $\omega=9.8$ rad/s. Neglecting initial vertical center-of-mass speed, free-fall time through 0.5 m is $\sqrt{1/g}$, giving $\theta=179.4$ degrees.

Official GATE 2026 answer key: https://gate2026.iitg.ac.in/doc/download/2026/Keys/PH_Keys.pdf