Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
JEE Main 202229 JulyMorning Shift
Exam
JEE Main
Year
2022
Date
29 July
Shift
Morning Shift
Subject
Physics
Chapter
Gravitation

JEE Main 2022 · 29 July · Morning Shift · Physics · Gravitation

If the acceleration due to gravity experienced by a point mass at a...

If the acceleration due to gravity experienced by a point mass at a height hh above the surface of earth is same as that of the acceleration due to gravity at a depth \alphah(h≪Re)\alphah\left(h ≪ {R}_{e}\right) ) from the earth surface. The value of α\alpha will be _____ .

(use Re=6400km{R}_{e} = 6400km)

Correct answer

0

Step-by-step solution

Acceleration due to gravity at a height hh above the earth's surface is given by gg\left(1 - \dfrac{2h}{{R}_{e}}\right)</p><p>Andaccelerationduetogravityatdepth</p><p>And acceleration due to gravity at depthdbelowtheearthsurfaceisgivenbybelow the earth surface is given byg\left(1 - \dfrac{d}{{R}_{e}}\right).</p><p>As.</p><p>As{g}_{above} = {g}_{below}</p><p>So,</p><p>So,g\left(1 - \dfrac{2h}{{R}_{e}}\right) = g\left(1 - \dfrac{d}{{R}_{e}}\right)</p><p></p><p>⇒ \dfrac{2h}{{R}_{e}} = \dfrac{d}{{R}_{e}}</p><p></p><p>⇒ \alphah = d</p><p>Thus,thevalueof</p><p>Thus, the value of\alpha = 2.

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