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Saturday, 31 October

JEE Main 2020 · PhysicsMultiple choiceDiagram basedHardMulti-step

JEE Main 3 September 2020, Shift 2, Physics Q4

Question 4 of 75 in this shift, Physics question 4 of 25.

A uniform rod of length 'l' is pivoted at one of its ends on a vertical shaft of negligible radius. When the shaft rotates at angular speed ω\omega the rod makes an angle θ\theta with it (see figure). To find θ\theta equate the rate of change of angular momentum (direction going into the paper) ml212ω2sin⁡θcos⁡θ\frac{ml^2}{12}\omega^2\sin\theta\cos\theta about the centre of mass (CM) to the torque provided by the horizontal and vertical forces FHF_H and FVF_V about the CM. The value of θ\theta is then such that :

The figure, in words

A thick vertical line (the shaft) with a curved arrow at its top labelled omega. A thin rod of length l is drawn hinged to the shaft near the top, sloping down and to the right, making angle theta with the shaft (angle marked between shaft and rod below the hinge). To the left of the shaft: F_V drawn as an upward arrow and F_H as a leftward arrow.
  1. (1)cos⁡θ=g2lω2\cos\theta = \frac{g}{2l\omega^2}
  2. (2)cos⁡θ=glω2\cos\theta = \frac{g}{l\omega^2}
  3. (3)cos⁡θ=3g2lω2\cos\theta = \frac{3g}{2l\omega^2}Official answer
  4. (4)cos⁡θ=2g3lω2\cos\theta = \frac{2g}{3l\omega^2}

Official answer

Option 3

NTA final key (Sep 2020).

Same idea in other shifts

Asked 2× in all
  1. 17 Mar 2021, Shift 1 · Q6A mass M hangs on a massless rod of length ll which rotates at a constant angular frequency. The mass M moves with steady speed in a…HardDiagram basedHas a figure

Question text from the official JEE Main paper published by NTA; answer from the final answer key. Chapter, topic and idea tags, difficulty and skill are Lumi’s. This question needs a figure we do not reproduce; it is described in words above. Lumi analyses 108 of the 174 JEE Main shifts held from 2017 to 2026.