MyQuestionIcon

1

You visited us 1 times! Enjoying our articles? Unlock Full Access!

Escape Speed

Three planets...

Question

Three planets of same density and with radii $R_{1}, R_{2}$ and $R_{3}$ , such that $R_{1} = 2 R_{2} = 3 R_{3},$ have gravitation fields on the surfaces $E_{1}, E_{2}, E_{3}$ and escape velocities $v_{1}, v_{2}, v_{3}$ respectively, Then

A

\frac{E_{1}}{E_{2}} = \frac{1}{2}

No worries! We‘ve got your back. Try BYJU‘S free classes today!

B

\frac{E_{1}}{E_{3}} = 3

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

C

\frac{v_{1}}{v_{2}} = 2

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

D

\frac{v_{1}}{v_{3}} = \frac{1}{3}

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct options are
B $\frac{v_{1}}{v_{2}} = 2$
C $\frac{E_{1}}{E_{3}} = 3$

$E = \frac{G M}{R^{2}}$ $= \frac{G (\frac{4}{3} π R^{3} ρ)}{R^{2}}$

$\Rightarrow E \propto R$

$\Rightarrow \frac{E_{1}}{E_{2}} = \frac{R_{1}}{R_{2}}$ $= 2$

$\Rightarrow (A)$ is not true

$\frac{E_{1}}{E_{3}} = \frac{R_{1}}{R_{3}}$ $= 3$

$\Rightarrow (B)$ is true

$v = \sqrt{g R} \Rightarrow v α R$

$\frac{v_{1}}{v_{2}} = \frac{R_{1}}{R_{2}} = 2$

$\Rightarrow (C)$ is true

$\frac{v_{1}}{v_{3}} = \frac{R_{1}}{R_{3}} = 3$

$\Rightarrow (D)$ is not true

Suggest Corrections

thumbs-up

0

Similar questions

Q. Three planets of same density have radii

R_{1}, R_{2}

R_{3}

R_{1} = 2 R_{2} = 3 R_{3}

The gravitational field at their respective surfaces are

g_{1}, g_{2}

g_{3}

and escape velocities from their surfaces are

v_{1}, v_{2}

v_{3}

Q. Two planets of same density and with radii

R_{1}

R_{2}

R_{1} = 2 R_{2}

have gravitation fields on the surface

g_{1}

g_{2}

and escape velocities

v_{1}

v_{2}

respectively. Then find the value of

\frac{v_{1}}{v_{2}}

Q. Two planets of same density, have radii

R_{1}

R_{2}

R_{1} = 2 R_{2}

. If the escape velocity on the planets are

v_{1}

v_{2}

respectively. Then ratio

\frac{v_{2}}{v_{1}}

E_{1}, E_{2}

E_{3}

respectively represent the kinetic energies of an electron, an

α

-particle and a proton each having same de-Broglie’s wavelength, then

E_{1}, E_{2} a n d E_{3}

represent respectively the kinetic energies of an electron, an alpha particle and a proton, each having same de-Broglie wavelength then?

View More

Join BYJU'S Learning Program

similar_icon

Related Videos

lock

Escape Velocity

PHYSICS

Watch in App

explore_more_icon

Explore more

Standard XII Physics

Join BYJU'S Learning Program

CrossIcon