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Saturday, 31 October

JEE Main 2020 · PhysicsMultiple choiceDiagram basedHardMulti-step

JEE Main 8 January 2020, Shift 2, Physics Q4

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

As shown in fig. when a spherical cavity (centred at O) of radius 1 is cut out of a uniform sphere of radius R (centred at C), the centre of mass of remaining (shaded) part of sphere is at G, i.e on the surface of the cavity. R can be determined by the equation :

The figure, in words

Large circle (sphere) shaded with horizontal lines; a smaller unshaded circle (cavity) inside it touching/near the right part of the large circle. A horizontal line through the points marked G, C, O (in that order from left to right, each a dot). Two short vertical segments drop from near the top onto the dots at C and O; a short horizontal bar at the top labelled 'R' spans to the vertical at C, and the vertical at O is labelled '1'.
  1. (1)(R2+R−1) (2−R)=1(R^2+R-1)\,(2-R)=1
  2. (2)(R2−R+1) (2−R)=1(R^2-R+1)\,(2-R)=1
  3. (3)(R2+R+1) (2−R)=1(R^2+R+1)\,(2-R)=1Official answer
  4. (4)(R2−R−1) (2−R)=1(R^2-R-1)\,(2-R)=1

Official answer

Option 3

NTA final key (Jan 2020).

Chapter
System of Particles and Rotational Motion
Topic
Center of Mass
Idea tested
COM of Cavity Bodies

Same idea in other shifts

Asked 3× in all
  1. 4 Aug 2021, Shift 1 · Q13Choose the correct option for the centre of mass of a uniform disc of radius ‘R’ from which a circular section of radius r (2r < R) has…MediumSingle correct
  2. 2 Sep 2020, Shift 2 · Q22A square shaped hole of side l=a2l = \frac{a}{2} is carved out at a distance d=a2d = \frac{a}{2} from the centre ‘O’ of a uniform circular…MediumNumerical valueHas 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.