Ratio of mass of Jupiter and Earth is 360 and ratio of their radii is 10. Then ratio of escape speed at Jupiter and Earth is

Open in App

Solution

Escape speed $V_{E} = \sqrt{\frac{2 G M}{R}}$

$V_{J} = \sqrt{\frac{2 G M_{J}}{R_{J}}}$ and $V_{E} = \sqrt{\frac{2 G M_{E}}{R_{E}}} \Rightarrow \frac{V_{J}}{V_{E}} = \sqrt{\frac{M_{J}}{M_{E}} (\frac{R_{E}}{R_{J}})}$
$\frac{V_{J}}{V_{E}} = \sqrt{\frac{360}{10}} = \sqrt{36} = 6$

Suggest Corrections

Similar questions

Q. The time periods of revolution of Earth and Jupiter are in the ratio 1:12. Then the radii of Jupiter and Earth are in the ratio .

The radius of Jupiter is 11 times the radius of earth. Calculate the ratio of the volume of Jupiter and earth. How many times earth can Jupiter accommodate?

Q. The radius of Jupiter is

11

times the radius of the Earth. Calculate the ratio of the volumes of Jupiter and the Earth. How many Earths can Jupiter accommodate?

Q. The planet Jupiter is

5

times farther from the sun than the earth, and the mass of Jupiter is

300

times the mass of the earth. If

F_{1}

is the gravitational force exerted by the sun on Jupiter, and

F_{2}

is the gravitational force exerted by the sun on the earth, Find out the value of the ratio

\frac{F_{1}}{F_{2}}

Join BYJU'S Learning Program

Ratio of mass of Jupiter and Earth is 360 and ratio of their radii is 10. Then ratio of escape speed at Jupiter and Earth is

Escape speed VE=√2GMR VJ=√2GMJRJ and VE=√2GMERE⇒VJVE=√MJME(RERJ) VJVE=√36010=√36=6

Escape speed $V_{E} = \sqrt{\frac{2 G M}{R}}$

$V_{J} = \sqrt{\frac{2 G M_{J}}{R_{J}}}$ and $V_{E} = \sqrt{\frac{2 G M_{E}}{R_{E}}} \Rightarrow \frac{V_{J}}{V_{E}} = \sqrt{\frac{M_{J}}{M_{E}} (\frac{R_{E}}{R_{J}})}$
$\frac{V_{J}}{V_{E}} = \sqrt{\frac{360}{10}} = \sqrt{36} = 6$