Question

planet x has mass twice that of earth the accelration due ot gravity on surface of this planet is half that on surface of earth. if earth ahs radius 1 what is radius of planet x

Answer 1

The radius of Planet X, with twice the mass of Earth and half the acceleration due to gravity, is approximately 1.414 times that of Earth if Earth's radius is considered as 1.

Step-by-step explanation:

To determine the radius of Planet X, which has twice the mass of Earth and half the acceleration due to gravity, we can use the formula for gravitational force, which is:

F = G * (m1*m2)/r^2

Since the gravitational force F on the surface of a planet equals the mass m of an object multiplied by the planet's acceleration due to gravity g (F = m * g), we can set the formula for gravity on Earth equal to that on Planet X:

gEarth = G * (massEarth)/radiusEarth^2

(1/2) * gEarth = G * (2 * massEarth)/radiusX^2

By simplifying and solving for radiusX, we find that the radius of Planet X must be:

radiusX = √2 * radiusEarth

Since the question mentioned that Earth has a radius of 1 (in unspecified units), the radius of Planet X is:

radiusX = √2 * 1

radiusX = √2 ≈ 1.414 (in the same unspecified units)