Which of the following most closely depicts the correct variation of the gravitation potential V(r) due to a large planet of radius R and uniform mass density ? (figures are not drawn to scale)

  • Option 1)

  • Option 2)

  • Option 3)

  • Option 4)

 

Answers (1)

As we learnt in

Potential due to Uniform solid sphere -

R\rightarrow Radius of sphere

M\rightarrow Mass of sphere

r\rightarrow distance from centre of sphere

Vcentre=\frac{3}{2}Vsurface

- wherein

Outside the surface

V=-\frac{GM}{r}

on the surface

Vsurface=-\frac{GM}{R}

Inside the surface 

r<R

V=-\frac{GM}{2R}\left[3-\left ( \frac{r}{R} \right )^{2}\right]

 

 Potential v\left | r \right |  due to a large planet of radius R

v_0 (r) = -\frac{Gm}{r},\: r>R

v(r) = -\frac{Gm}{R},\: r=R

v_{in} = -\frac{3}{2}\frac{Gm}{R}[1-\frac{r^2}{3R^2}];\;\ r < R


Option 1)

Incorrect

Option 2)

Correct

Option 3)

Incorrect

Option 4)

Incorrect

Most Viewed Questions

Preparation Products

Knockout JEE Main April 2021 (One Month)

Personalized AI Tutor and Adaptive Time Table, Self Study Material, Weekend Live Classes, Unlimited Mock Tests and Personalized Analysis Reports, 24x7 Doubt Chat Support,.

₹ 14000/- ₹ 4999/-
Buy Now
Knockout JEE Main May 2021

Personalized AI Tutor and Adaptive Time Table, Self Study Material, Weekend Live Classes, Unlimited Mock Tests and Personalized Analysis Reports, 24x7 Doubt Chat Support,.

₹ 22999/- ₹ 9999/-
Buy Now
Test Series JEE Main May 2021

Unlimited Chapter Wise Tests, Unlimited Subject Wise Tests, Unlimited Full Mock Tests, Get Personalized Performance Analysis Report,.

₹ 6999/- ₹ 2999/-
Buy Now
Knockout JEE Main May 2022

Personalized AI Tutor and Adaptive Time Table, Self Study Material, Live Classes, Unlimited Mock Tests and Personalized Analysis Reports, 24x7 Doubt Chat Support,.

₹ 34999/- ₹ 24999/-
Buy Now
JEE Main Rank Booster 2021

Booster and Kadha Video Lectures, Unlimited Full Mock Test, Adaptive Time Table, 24x7 Doubt Chat Support,.

₹ 13999/- ₹ 6999/-
Buy Now
Boost your Preparation for JEE Main 2021 with Personlized Coaching
 
Exams
Articles
Questions