Question

Planets A and B have the same size, mass, and direction of travel, but planet A is traveling through space at half the speed of planet B. Which statement correctly explains the weight you would experience on each planet? A. You would weigh less on planet B because it is traveling twice as fast as planet A. B. You would weigh the same on both planets because their masses and the distance to their centers of gravity are the same. O C. You would weigh more on planet B because it is traveling twice as fast as planet A. D. You would weigh the same on both planets because your mass would adjust depending on the planet's speed.​

Answer 1

Answer:

B. You would weigh the same on both planets because their masses and the distance to their centers of gravity are the same.

Explanation:

Given that Planets A and B have the same size, mass.

Let the masses of the planets A and B are $m_A$ and $m_B$ respectively.

As masses are equal, so $m_A=m_B\cdots(i)$.

Similarly, let the radii of the planets A and B are $r_A$ and $r_B$ respectively.

As radii are equal, so $r_A=r_B\cdots(ii)$.

Let my mass is m.

As the weight of any object on the planet is equal to the gravitational force exerted by the planet on the object.

So, my weight on planet A, $w_A= \frac {Gm_Am}{r_A^2}$

my weight of planet B, $w_B=\frac {Gm_Bm}{r_B^2}$

By using equations (i) and (ii),

$w_B=\frac {Gm_Am}{r_A^2}=w_A$.

So, the weight on both planets is the same because their masses and the distance to their centers of gravity are the same.

Hence, option (B) is correct.