The escape velocity from the… - NEET UG 2021 Physics PYQ

NEET UG 2021 — Physics Mechanics

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The escape velocity from the Earth's surface is $v$ . The escape velocity from the surface of another planet having a radius four times that of Earth and the same mass density is:

Official previous-year question

Held on 30 Apr 2021 · Verified 9 Jul 2026.

Options

A
$v$
B
$2v$
C
$3v$
D
$4v$

Did you get this right?

Solution

Given,

Escape velocity from earth's surface $=v$

$v={v}_{earth}=\sqrt{2gR}$

$=\sqrt{\frac{2GM}{\frac{4}{3}\pi {R}^{3}}\frac{4}{3}\pi {R}^{2}}=\sqrt{\frac{2GM}{V}\frac{4}{3}\pi {R}^{2}}=\sqrt{\frac{8G\rho \pi {R}^{2}}{3}}$

$g=$ Gravitation acceleration on earth surface

$R=$ Radius of earth

$G=$ Universal gravitational constant

Escape velocity of another planet $=?$

$\because {R}_{p}=4R &$

${\rho }_{planet}={\text{ρ}}_{earth}$

So we can write,

${v}_{e}\propto \sqrt{{R}^{2}}\propto R$

$\frac{{({v}_{e})}_{earth}}{{({v}_{e})}_{planet}}=\frac{{R}_{earth}}{{R}_{planet}}=\frac{R}{4R}=\frac{1}{4}$

It means,

$4{({v}_{e})}_{earth}={({v}_{e})}_{Planet}$

${({v}_{e})}_{Planet}=4v$

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Solution

Given,

Escape velocity from earth's surface $=v$

$v={v}_{earth}=\sqrt{2gR}$

$=\sqrt{\frac{2GM}{\frac{4}{3}\pi {R}^{3}}\frac{4}{3}\pi {R}^{2}}=\sqrt{\frac{2GM}{V}\frac{4}{3}\pi {R}^{2}}=\sqrt{\frac{8G\rho \pi {R}^{2}}{3}}$

$g=$ Gravitation acceleration on earth surface

$R=$ Radius of earth

$G=$ Universal gravitational constant

Escape velocity of another planet $=?$

$\because {R}_{p}=4R &$

${\rho }_{planet}={\text{ρ}}_{earth}$

So we can write,

${v}_{e}\propto \sqrt{{R}^{2}}\propto R$

$\frac{{({v}_{e})}_{earth}}{{({v}_{e})}_{planet}}=\frac{{R}_{earth}}{{R}_{planet}}=\frac{R}{4R}=\frac{1}{4}$

It means,

$4{({v}_{e})}_{earth}={({v}_{e})}_{Planet}$

${({v}_{e})}_{Planet}=4v$

Options

Did you get this right?

Solution

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Options

Did you get this right?

Solution

Your note

NEET UG Mechanics in other years

More NEET UG Mechanics questions

Other Physics topics for NEET UG

Electromagnetism

Modern Physics

Thermodynamics

Optics

Waves & Oscillations

Keep practicing Mechanics