Sign in
12thPass logo
New chatPYQ LibraryDoubtsRank report
Sign in to see Recents

Your guest activity stays on this device

Sign in to save progress →
Sign in

Gravitation question

2020 · 9 Jan · Shift 2 · Q49
Guest · filters and generic practice availableBrowsing as a guest · PYQ filters and generic practice are available. Sign in only for personalised features and saved progress.
  1. PYQ Library
  2. /JEE Main
  3. /Physics
  4. /Gravitation
  5. /2020 · 9 Jan · Shift 2 · Q49

Gravitation question

2020 · 9 Jan · Shift 2 · Q49

JEE MainPhysicsGravitationMCQ+4 / −1
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}vB​vA​​=4n​. The value of n is :
  1. A
    1
  2. B
    2
  3. C
    4
  4. D
    3
View written solutionFree

Correct answer: C

  1. Use the escape velocity formula

For a planet of mass MMM and radius RRR, escape velocity is

ve=2GMRv_e = \sqrt{\frac{2GM}{R}}ve​=R2GM​​

  1. Escape velocity of Planet A

Planet A has mass MMM and radius RRR, so

vA=2GMRv_A = \sqrt{\frac{2GM}{R}}vA​=R2GM​​

  1. Escape velocity of Planet B

Planet B has:

  • mass =M2= \dfrac{M}{2}=2M​
  • radius =R2= \dfrac{R}{2}=2R​

So,

vB=2G(M/2)R/2v_B = \sqrt{\frac{2G(M/2)}{R/2}}vB​=R/22G(M/2)​​

Simplify inside the root:

2G(M/2)R/2=2G⋅M2⋅2R=2GMR\frac{2G(M/2)}{R/2} = 2G \cdot \frac{M}{2} \cdot \frac{2}{R} = \frac{2GM}{R}R/22G(M/2)​=2G⋅2M​⋅R2​=R2GM​

Hence,

vB=2GMRv_B = \sqrt{\frac{2GM}{R}}vB​=R2GM​​

  1. Find the ratio

vAvB=2GM/R2GM/R=1\frac{v_A}{v_B} = \frac{\sqrt{2GM/R}}{\sqrt{2GM/R}} = 1vB​vA​​=2GM/R​2GM/R​​=1

Given,

vAvB=n4\frac{v_A}{v_B} = \frac{n}{4}vB​vA​​=4n​

So,

n4=1  ⟹  n=4\frac{n}{4} = 1 \implies n = 44n​=1⟹n=4

  1. Check options
  • A: 111
  • B: 222
  • C: 444 ✅
  • D: 333

Therefore, the correct option is C.

PreviousNext

More from Gravitation

  • Four identical particles of mass M are located at the corners of a square of side 'a'. What should be their speed if each of them revolves under the influence of other's gravitational field in a circular orbit circumscribing the square? Includes diagram2019 · MCQ
  • A rocket has to be launched from earth in such a way that it never returns. If E is the minimum energy delivered by the rocket launcher, what should be the minimum energy that the launcher should have if the same rocket is to be launched…2019 · MCQ
  • A solid sphere of mass 'M' and radius 'a' is surrounded by a uniform concentric spherical shell of thickness 2a and mass 2M. The gravitational field at distance '3a' from the centre will be :2019 · MCQ
  • A test particle is moving in a circular orbit in the gravitational field produced by a mass density ρ(r)=r2K​ . Identify the correct relation between the radius R of the particle's orbit and its period T2019 · MCQ
  • The energy required to take a satellite to a height 'h' above Earth surface (radius of Earth = 6.4 × 103 km) is E1 and kinetic energy required for the satellite to be in a circular orbit at this height is E2. The value of h for…2019 · MCQ
  • The value of acceleration due to gravity at Earth's surface is 9.8 ms–2. The altitude above its surface at which the acceleration due to gravity decreases to 4.9 ms–2, is close to : (Radius of earth = 6.4 × 106 m)2019 · MCQ
  • A spaceship orbits around a planet at a height of 20 km from its surface. Assuming that only gravitational field of the planet acts on the spaceship, what will be the number of complete revolutions made by the spaceship in 24 hours around…2019 · MCQ
  • A satellite is moving with a constant speed v in circular orbit around the earth. An object of mass ‘m’ is ejected from the satellite such that it just escapes from the gravitational pull of the earth. At the time of ejection, the kinetic…2019 · MCQ