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Friday, 9 October

JEE Main 2020 · PhysicsMultiple choiceSingle correctEasyCalculation

JEE Main 9 January 2020, Shift 2, Physics Q5

Question 5 of 75 in this shift, Physics question 5 of 25, Section A.

A rod of length LL has non-uniform linear mass density given by ρ(x)=a+b(xL)2\rho(x) = a + b\left(\frac{x}{L}\right)^2, where aa and bb are constants and 0≤x≤L0 \le x \le L. The value of xx for the centre of mass of the rod is at :
  1. (1)34(2a+b3a+b)L\frac{3}{4}\left(\frac{2a+b}{3a+b}\right)LOfficial answer
  2. (2)32(2a+b3a+b)L\frac{3}{2}\left(\frac{2a+b}{3a+b}\right)L
  3. (3)43(a+b2a+3b)L\frac{4}{3}\left(\frac{a+b}{2a+3b}\right)L
  4. (4)32(a+b2a+b)L\frac{3}{2}\left(\frac{a+b}{2a+b}\right)L

Official answer

Option 1

NTA final key (Jan 2020).

Chapter
System of Particles and Rotational Motion
Topic
Center of Mass
Idea tested
COM of Non-Uniform Rod

Same topic in other shifts

All Center of Mass questions
  1. 2 Apr 2026, Shift 2 · Q28Two blocks of masses 2 kg and 1 kg respectively, are tied to the ends of a string which passes over a light frictionless pulley as shown…MediumSingle correctHas a figure
  2. 6 Apr 2026, Shift 1 · Q33The position of center of mass of three masses 2 kg, 3 kg and 15 kg placed with respect to mid point (pp) of normal bisector, as shown in…EasySingle correctHas a figure
  3. 6 Apr 2026, Shift 2 · Q32Two identical bodies A and B of equal masses have initial velocities v⃗1=4i^\vec{v}_1=4\hat{i} m/s and v⃗2=4j^\vec{v}_2=4\hat{j} m/s respectively.…MediumSingle correct
  4. 7 Apr 2025, Shift 1 · Q29A rod of length 5 L is bent right angle keeping one side length as 2 L. The position of the centre of mass of the system: (Consider L = 10…EasySingle correctHas a figure
  5. 8 Apr 2024, Shift 1 · Q52A uniform thin metal plate of mass 10 kg with dimensions is shown. The ratio of xx and yy coordinates of center of mass of plate in…MediumNumerical valueHas a figure
  6. 25 Jul 2021, Shift 1 · Q21A body of mass 2 kg moving with a speed of 4 m/s. makes an elastic collision with another body at rest and continues to move in the…MediumNumerical value

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. Lumi analyses 42 of the 174 JEE Main shifts held from 2017 to 2026.