Question

A small body of superdense material, whose mass is twice the mass of the earth but whose size is very small compared to the size of the earth, starts from rest at a height h<

Answer 1

Solution :- you know about Newton's 3rd law of motion " action and reaction are of equal in magnitude but directed in opposite direction. "
here super dense mass comes downward then earth moves upward. Both body meet at a point . This point is center of mass.

So , first of all we have to find out centre of mass .
∴ centre of mass with respect to earth = {mass of material × distance of material from earth surface + mass of earth × 0}/(mass of material + mass of earth)
Given, mass of material = 2M
Mass of earth = M
∴ C.O.M with respect to earth = 2m × H/(2m + m) = 2H/3
It means actual distance is covered by body = H - H/3 = H/3

Now, use formula,
S = ut + 1/2at²
H/3 = 0 + 1/2gt²
t² = 2H/3g
t = √{2H/3g}

Hence, answer is T = √{2H/3g}

Answer 2

Answer:

$t = \sqrt{ \frac{2h}{3g} }$

Explanation:

For explanation, please refer to the given attachments.