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Friday, 9 October

JEE Main 2020 · PhysicsMultiple choiceSingle correctMediumCalculation

JEE Main 6 September 2020, Shift 2, Physics Q5

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

The linear mass density of a thin rod AB of length L varies from A to B as λ(x)=λ0(1+xL)\lambda(x)=\lambda_0\left(1+\frac{x}{L}\right), where xx is the distance from A. If M is the mass of the rod then its moment of inertia about an axis passing through A and perpendicular to the rod is :
  1. (1)512ML2\frac{5}{12}ML^2
  2. (2)718ML2\frac{7}{18}ML^2Official answer
  3. (3)25ML2\frac{2}{5}ML^2
  4. (4)37ML2\frac{3}{7}ML^2

Official answer

Option 2

NTA final key (Sep 2020).

Chapter
System of Particles and Rotational Motion
Topic
Moment of Inertia
Idea tested
MOI with Linear Density Gradient

Same topic in other shifts

All Moment of Inertia questions
  1. 2 Apr 2026, Shift 2 · Q50Moment of inertia about an axis ABAB for a rod of mass 40 kg and length 3 m is same as that of a solid sphere of mass of 10 kg and radius…MediumNumerical valueHas a figure
  2. 4 Apr 2026, Shift 1 · Q30A solid sphere of mass MM and radius RR is divided into two unequal parts. The smaller part having mass M/8M/8 is converted into a sphere…MediumSingle correct
  3. 6 Apr 2026, Shift 1 · Q31A solid sphere of radius 4 cm and mass 5 kg is rotating (rotation axis is passing through the centre of the sphere) with an angular…MediumSingle correct
  4. 2 Apr 2025, Shift 1 · Q32Moment of inertia of a rod of mass 'M' and length 'L' about an axis passing through its center and normal to its length is 'α\alpha'. Now…MediumSingle correct
  5. 2 Apr 2025, Shift 2 · Q28The moment of inertia of a circular ring of mass MM and diameter rr about a tangential axis lying in the plane of the ring is :EasySingle correct
  6. 7 Apr 2025, Shift 1 · Q46A, B and C are disc, solid sphere and spherical shell respectively with same radii and masses. These masses are placed as shown in figure.…HardNumerical 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. Lumi analyses 42 of the 174 JEE Main shifts held from 2017 to 2026.