Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
JEE Main 202131 AugustMorning Shift
Exam
JEE Main
Year
2021
Date
31 August
Shift
Morning Shift
Subject
Physics
Chapter
Gravitation

JEE Main 2021 · 31 August · Morning Shift · Physics · Gravitation

The masses and radii of the earth and moon are ( M _ 1 , R _ 1 )...

The masses and radii of the earth and moon are (M1,R1)\left({M}_{1}, {R}_{1}\right) and (M2,R2)\left({M}_{2}, {R}_{2}\right) respectively. Their centres are at a distance rr apart. Find the minimum escape velocity for a particle of mass mm to be projected from the middle of these two masses :The masses and radii of the earth and moon are ( M _ 1 , R _ 1 ) and ( M _ 2 , R _ 2 ) respectively. Their centres are

Options

  1. A{v}_{e} = \sqrt{\dfrac{4G\left({M}_{1} + {M}_{2}\right)}{r}}
  2. B{v}_{e} = \dfrac{1}{2}\sqrt{\dfrac{2G\left({M}_{1} + {M}_{2}\right)}{r}}
  3. C{v}_{e} = \dfrac{1}{2}\sqrt{\dfrac{4G\left({M}_{1} + {M}_{2}\right)}{r}}
  4. D{v}_{e} = \dfrac{\sqrt{2G}\left({M}_{1} + {M}_{2}\right)}{r}

Correct answer

A. {v}_{e} = \sqrt{\dfrac{4G\left({M}_{1} + {M}_{2}\right)}{r}}

Step-by-step solution

The masses and radii of the earth and moon are ( M _ 1 , R _ 1 ) and ( M _ 2 , R _ 2 ) respectively. Their centres are

On conserving mechanical energy. The initial total energy is equal to final total energy, ⇒−(GM1r2+GM2r2)m+12mve2=0⇒ - \left(\dfrac{G{M}_{1}}{\dfrac{r}{2}} + \dfrac{G{M}_{2}}{\dfrac{r}{2}}\right)m + \dfrac{1}{2}m{v}_{e}^{2} = 0
⇒ve=4G(M1+M2)r⇒ {v}_{e} = \sqrt{\dfrac{4G\left({M}_{1} + {M}_{2}\right)}{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