Browse by Stream
QnA
Home
QnA
Go To Your Study Dashboard

Get Answers to all your Questions

header-bg qa
  • Home
  • Medical
  • Consider a thin uniform spherical layer of mass and radius <img alt="\mathrm{R}" src="https://entranc

Consider a thin uniform spherical layer of mass \mathrm{M} and radius \mathrm{R}, if we consider a solid sphere of mass \mathrm{M} and radius \mathrm{R}, then the potential energy of gravitational interaction of matter forming this solid sphere is
 

Option: 1

\mathrm{-\frac{\mathrm{GM}^2}{\mathrm{R}}}


 


Option: 2

-\frac{1}{2} \frac{\mathrm{GM}^2}{\mathrm{R}}
 


Option: 3

-\frac{3}{5} \frac{\mathrm{GM}^2}{\mathrm{R}}
 


Option: 4

-\frac{3}{2} \frac{\mathrm{GM}^2}{\mathrm{R}}


Answers (1)

best_answer

\mathrm{ d U=-\frac{\mathrm{Gmdm}}{\mathrm{r}} }

\mathrm{ \Rightarrow \mathrm{dU}=-\frac{\mathrm{G}\left(\frac{4}{3} \pi r^3 \rho\right)\left(4 \pi r^2 \mathrm{dr} \rho\right)}{\mathrm{r}} }

\mathrm{ \Rightarrow \mathrm{dU}=-\frac{16 \pi^2 \mathrm{G} \rho^2}{3} \mathrm{r}^4 \mathrm{dr} }

\mathrm{ \Rightarrow \mathrm{U}=-\frac{16}{3} \pi^2 \mathrm{G}\left(\frac{\mathrm{M}}{\frac{4}{3} \pi \mathrm{R}^3}\right)^2 \int_0^{\mathrm{R}} \mathrm{r}^4 \mathrm{dr} }

\mathrm{ \Rightarrow \mathrm{U}=-\left(\frac{16}{3} \pi^2 \mathrm{G}\right)\left(\frac{\mathrm{M}^2}{\frac{16}{9} \pi^2 \mathrm{R}^6}\right)\left(\frac{\mathrm{R}^5}{5}\right) }

\mathrm{ \Rightarrow \mathrm{U}=-\frac{3}{5} \frac{\mathrm{GM}^2}{\mathrm{R}}}

Hence option 3 is correct.





 

Posted by

Info Expert 30

View full answer

NEET 2024 Most scoring concepts

    Just Study 32% of the NEET syllabus and Score up to 100% marks

Similar Questions

Trending Articles/News

anam-khan

'PM Modi personally supervising the situation': Centre tells SC in NEET case
anam-khan

NEET Paper Leak Row: NTA informs SC of security overhaul, institutional reforms
anam-khan

Re-NEET 2026 City Intimation Slip LIVE: NTA MBBS admit card soon; direct link, login details, exam date

Latest Question