Physics, 20.02.2020 02:03 isamar4348

A hypothetical planet has a mass one-third of and a radius three times that of earth. What is the acceleration due to gravity on the planet in terms of g

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Answer from: itsyourboyrocky

Acceleration of gravity on the planet is $\frac{g}{27}$

Explanation:

The acceleration of gravity at the surface of a planet is given by

$g=\frac{GM}{R^2}$

where

G is the gravitational constant

M is the mass of the planet

R is the radius of the planet

For the Earth, we have

$g_E = \frac{GM_E}{R_E^2}$

where M_E is the Earth mass and R_E is the Earth's radius.

For the planet in this problem, we have

$M_X = \frac{1}{3}M_E$ (mass is 1/3 of the Earth)

R_X=3R_E (radius is 3 times that of Earth)

Therefore, its acceleration of gravity is

$g_X = \frac{GM_X}{R_X^2}=\frac{G(\frac{1}{3}M_E)}{(3R_E)^2}=\frac{1}{27}(\frac{GM_E}{R_E^2})=\frac{g_E}{27}$

Answer from: Quest

Hypothesis. why don’t you know this? i learned this stuff in like 5th grade

Answer from: Quest

force is based upon mass and acceleration.the statement is not always true.

it can be explained from newton's second law of motion.

as per newton's second law of motion the rate of change of momentum is directly proportional to the applied force and takes place along the direction of force.

mathematically it can be written as -

$f\alpha \frac{dp}{dt}$

⇒ $f= k \frac{dp}{dt}$

here k is the proportionality constant whose value is 1.

$f=\frac{dp}{dt}$

$f= \frac{d[mv]}{dt}$

$f= m\frac{dv}{dt} +v\frac{dm}{dt}$

$f=ma+v\frac{dm}{dt}$ [a is the acceleration=dv/dt]

hence we see that force not only depends on mass and acceleration but also on velocity and rate of change of mass. force f will depend on mass and acceleration only when mass is constant.

hence the statement that force is based upon mass and acceleration is false.

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A hypothetical planet has a mass one-third of and a radius three times that of earth. What is the ac...

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