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Saturday, 31 October

JEE Main 2021 · PhysicsMultiple choiceSingle correctHardMulti-step

JEE Main 22 July 2021, Shift 2, Physics Q12

Question 12 of 90 in this shift, Physics question 12 of 30, Section A.

A body is projected vertically upwards from the surface of earth with a velocity sufficient enough to carry it to infinity. The time taken by it to reach height h is ________ s.
  1. (1)13Re2g[(1+hRe)3/2−1]\frac{1}{3}\sqrt{\frac{R_e}{2g}}\left[\left(1+\frac{h}{R_e}\right)^{3/2}-1\right]
  2. (2)132Reg[(1+hRe)3/2−1]\frac{1}{3}\sqrt{\frac{2R_e}{g}}\left[\left(1+\frac{h}{R_e}\right)^{3/2}-1\right]Official answer
  3. (3)Re2g[(1+hRe)3/2−1]\sqrt{\frac{R_e}{2g}}\left[\left(1+\frac{h}{R_e}\right)^{3/2}-1\right]
  4. (4)2Reg[(1+hRe)3/2−1]\sqrt{\frac{2R_e}{g}}\left[\left(1+\frac{h}{R_e}\right)^{3/2}-1\right]

Official answer

Option 2

NTA final key.

Chapter
Gravitation
Topic
Orbital Mechanics
Idea tested
Escape Velocity

Same idea in other shifts

Asked 8× in all
  1. 30 Jan 2024, Shift 2 · Q36Escape velocity of a body from earth is 11.2 km/s11.2\ km/s. If the radius of a planet be one-third the radius of earth and mass be one-sixth…EasySingle correct
  2. 31 Jan 2024, Shift 2 · Q36The mass of the moon is 1144\frac{1}{144} times the mass of a planet and its diameter is 116\frac{1}{16} times the diameter of a planet. If…EasySingle correct
  3. 12 Apr 2023, Shift 1 · Q36The ratio of escape velocity of a planet to the escape velocity of earth will be:- Given: Mass of the planet is 16 times mass of earth and…EasySingle correct
  4. 13 Apr 2023, Shift 2 · Q35Given below are two statements: Statement I : For a planet, if the ratio of mass of the planet to its radius increases, the escape…EasyTwo statements
  5. 29 Jun 2022, Shift 1 · Q44The escape velocity of a body on a planet 'A' is 12 kms−112\ \mathrm{kms^{-1}}. The escape velocity of the body on another planet 'B', whose…EasySingle correct
  6. 3 Aug 2021, Shift 2 · Q6A particle is projected from the mid-point of the line joining two fixed particles each of mass mm in free space. If the separation…HardSingle correct
  7. 9 Jan 2020, Shift 2 · Q7Planet A has mass MM and radius RR. Planet B has half the mass and half the radius of Planet A. If the escape velocities from the…EasySingle 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 108 of the 174 JEE Main shifts held from 2017 to 2026.