Question

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 same mass density is​

Answer 1

Answer:

It would be 1/16 times the velocity as the distance is squared in the formula for calculating gravity.

g=Gx m1 x m2/ r square.

pls mark as brainliest, need some to rank up.

Answer 2

Given: Escape velocity from earth's surface is v. Another planet has radius 4 times that of earth but same mass density as that of earth

To find: Escape velocity from the another planet

Explanation: Let mass of earth be m1 and mass of another planet be m2.

It is given that radius of planet is 4 times that of earth. Therefore, r2= 4r1 where r2 is radius of another planet. We can write r1/r2= 1/4

Since mass density is same:

m1/r1^3= m2/ r2^3

=> m1/m2 = (r1/r2)^3

=> m1/m2 = (1/4)^3

=> 64m1 = m2

Now, escape velocity from earth is given by

$\sqrt{ \frac{2Gm1 }{r1} } = v$

Now, for another planet,

$\sqrt{ \frac{2G \times 64m1}{4r2} }$

= 4 $\sqrt{ \frac{2Gm1}{r1} }$

= 4v

Therefore, the escape velocity from the another planet is 4v.