Suppose the mass of the Earth were tripled, but it kept the same density and spherical shape. How would the weight of objects at the Earth's surface change?

Explanation:

Assume the earth is a sphere

Tripling the mass at the same density will triple the volume.

If R is earth radius

             V = (4/3)πR³

           3V = (4/3)πR₁³

3(4/3)πR³ = (4/3)πR₁³

         3R³ = R₁³

    (∛3)R = R₁

Gravity on earth is

g = GM/R²

Gravity on the new planet is

g₁ = GM₁/R₁²

g₁ = G(3M)/((∛3)R)²

g₁ = 3/(∛3)²GM/R²

g₁ = 3/(∛3)²g

so the weight of objects will be about 1.44 times greater

i wanna say it’s between b and d, leaning more towards b.

russian is not my first language, so i'm afraid i can't write out an answer in russian, but hopefully you can find a way to do so. here's my best translation of the problem: you're given a plot of a particle's position in one-dimensional space over time, and you're asked to find either the total distance traveled by the particle after 6 seconds had elapsed, or the total displacement of the particle after 6 seconds.

if you want the total distance traveled, you would first need to determine the particle's velocity as a function of time, then integrate that over the 6-second interval. we know the position function is quadratic with roots at 0 and 6, so we have

where is unknown. because the position is parabolic, there is symmetry about the midpoint at , and we know that

so that the position function is

which means the velocity is

then the total distance traveled is

so the total distance traveled is 20 m.

on the other hand, if you want to find displacement: the particle starts at and ends at , so its displacement is 0.