Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
JEE Main 20202 SeptemberEvening Shift
Exam
JEE Main
Year
2020
Date
2 September
Shift
Evening Shift
Subject
Physics
Chapter
Gravitation

JEE Main 2020 · 2 September · Evening Shift · Physics · Gravitation

The height ‘ h ’ at which the weight of a body will be...

The height ‘hh’ at which the weight of a body will be the same as that at the same depth ‘h’ from the surface of the earth is (Radius of the earth is RR and effect of the rotation of the earth is neglected)

Options

  1. A52R−R\dfrac{\sqrt{5}}{2}R - R
  2. BR2\dfrac{R}{2}
  3. C5R−R2\dfrac{\sqrt{5}R - R}{2}
  4. D3R−R2\dfrac{\sqrt{3}R - R}{2}

Correct answer

C. 5R−R2\dfrac{\sqrt{5}R - R}{2}

Step-by-step solution

GM(R+h)2=GMR3(R−h)\dfrac{GM}{( R + h{)}^{2}} = \dfrac{GM}{{R}^{3}} ( R - h )
R3=(R+h)2(R−h){R}^{3} = ( R + h{)}^{2} ( R - h )
=(R2+h2+2hR)(R−h)= \left({R}^{2} + {h}^{2} + 2hR\right) ( R - h )
R3=R3+h2R+2hR2−R2h−h3−2h2R{R}^{3} = {R}^{3} + {h}^{2}R + 2{hR}^{2} - {R}^{2}h - {h}^{3} - 2{h}^{2}R
h3+h2(2R−R)−R2h=0{h}^{3} + {h}^{2} ( 2R - R ) - {R}^{2}h = 0
h3+h2R−R2h=0{h}^{3} + {h}^{2}R - {R}^{2}h = 0
h2+hR−R2=0{h}^{2} + hR - {R}^{2} = 0
h=−R±R2+4(1)R22h = \dfrac{- R \pm \sqrt{{R}^{2} + 4 ( 1 ) {R}^{2}}}{2}
=−R+5R2= \dfrac{- R + \sqrt{5}R}{2}
=(5−1)2R= \dfrac{( \sqrt{5} - 1 )}{2}R
Practice Gravitation on Quantrex Academy →

More from Gravitation

A particle of mass m , and angular momentum ℓ is moving in a circular orbit of radius r_0… JEE Advanced 2026A body of mass m is taken from the surface of earth to a height equal to twice the radius… JEE Main 2026When one moves from a point 16 km below the earth's surface to a point 16 km above the… JEE Main 2026The height in terms of radius of the earth (R) , at which the acceleration due to gravity… JEE Main 2026If a body of mass 1 kg falls on the earth from infinity, it attains velocity (v) and… JEE Main 2026A planet (P_1) is moving around the star of mass 2M in the orbit of radius R . Another… JEE Main 2026Three masses 200 ~kg, 300 ~kg and 400 kg are placed at the vertices of an equilateral… JEE Main 2026Given below are two statements: Statement I : A satellite is moving around earth in the… JEE Main 2026 Full Gravitation list All JEE Main PYQs