Verified Solution • 2025–26 Session moderate

QJEEM20Phb07d: JEE Main 2020 Physics - Class 11 JEEM20Phb07d Solution: Planet A has mass M and radius R. Planet B has half the mass…

Planet A has mass M and radius R. Planet B has half the mass and half the radius of Planet A. If the escape velocities from the Planets A and B are vA and vB, respectively, then vAvB=n4{{{v_A}} \over {{v_B}}} = {n \over 4} . The value of n is :

Multiple Choice Options

  • A 1
  • B 2
  • C 4
  • D 3

Step-by-Step Verified Solution

Escape velocity, Ve = 2GMR\sqrt {{{2GM} \over R}}

VA = 2GMR\sqrt {{{2GM} \over R}}

VB = 2GM2R2\sqrt {{{2G{M \over 2}} \over {{R \over 2}}}} = 2GMR\sqrt {{{2GM} \over R}}

VAVB{{{V_A}} \over {{V_B}}} = 1

Given VAVB=n4{{{V_A}} \over {{V_B}}} = {n \over 4}

∴\therefore n4{n \over 4} = 1

⇒\Rightarrow n = 4

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