Browse by Stream
QnA
Home
QnA
Go To Your Study Dashboard

Get Answers to all your Questions

header-bg qa
  • Home
  • Medical
  • A body of mass m is approaching towards the centre of a hypothetical hollow planet of mass M and radius R. The speed of the body when it passes the centre of the planet through its diametrical chut

A body of mass m is approaching towards the centre of a hypothetical hollow planet of mass M and radius R. The speed of the body when it passes the centre of the planet through its diametrical chute is

Option: 1

\mathrm{\sqrt{\frac{G M}{R}}}


Option: 2

\mathrm{\sqrt{\frac{2G M}{R}}}


Option: 3

Zero


Option: 4

none of these.


Answers (1)

best_answer

At infinity, the total energy of the body is zero. Therefore the total energy of the body just before hitting the planet P will be zero according to the conservation of energy

\mathrm{\begin{aligned} & \Rightarrow \mathrm{F}_{\mathrm{p}}=\mathrm{E}_{\infty}=0 \quad \Rightarrow \quad \mathrm{U}_{\mathrm{p}}+\mathrm{K}_{\mathrm{p}}=0 \\ & \Rightarrow-\frac{\mathrm{GMm}}{\mathrm{R}}+\frac{1}{2} \mathrm{mv}^2=0 \\ & \Rightarrow \mathrm{v}=\sqrt{\frac{2 \mathrm{GM}}{\mathrm{R}}} . \end{aligned}}

Since the force imparted on a particle inside spherical shell is zero, therefore the velocity of the particle inside the spherical shell remain constant. Therefore, the body passes the centre of the planet with same speed \mathrm{v=\sqrt{\frac{2 \mathrm{GM}}{\mathrm{R}}}} .

Therefore (B).

Posted by

Rishabh

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

Karnataka: NEET candidate dies by suicide; no note recovered
anam-khan

CBSE Re-evaluation Row: Dharmendra Pradhan seeks detailed report on technical failures
anam-khan

Before NEET, CMC Vellore’s unique MBBS admissions tested aptitude along with merit; paper-leak restarts debate

Latest Question