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Friday, 9 October

JEE Main 2024 · PhysicsMultiple choiceSingle correctMediumMulti-step

JEE Main 9 April 2024, Shift 1, Physics Q37

Question 37 of 90 in this shift, Physics question 7 of 30, Section A.

A sphere of relative density σ\sigma and diameter D has concentric cavity of diameter d. The ratio of Dd\frac{D}{d}, if it just floats on water in a tank is :
  1. (1)(σ−1σ)1/3\left(\frac{\sigma-1}{\sigma}\right)^{1/3}
  2. (2)(σσ−1)1/3\left(\frac{\sigma}{\sigma-1}\right)^{1/3}Official answer
  3. (3)(σ−2σ+2)1/3\left(\frac{\sigma-2}{\sigma+2}\right)^{1/3}
  4. (4)(σ+1σ−1)1/3\left(\frac{\sigma+1}{\sigma-1}\right)^{1/3}

Official answer

Option 2

NTA final key.

Chapter
Mechanical Properties of Fluids
Topic
Fluid Statics
Idea tested
Law of Floatation

Same idea in other shifts

Asked 3× in all
  1. 2 Apr 2026, Shift 1 · Q50A tub is filled with water and a wooden cube 10 cm×10 cm×10 cm10\ \mathrm{cm}\times10\ \mathrm{cm}\times10\ \mathrm{cm} is placed in the water. The…EasyNumerical value
  2. 8 Jan 2020, Shift 1 · Q6Consider a solid sphere of radius R and mass density ρ(r)=ρ0(1−r2R2)\rho(r) = \rho_0\left(1-\frac{r^2}{R^2}\right), 0<r≤R0 < r \le R. The minimum density…HardSingle correct

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.