To develop this problem it is necessary to apply the concepts related to Gravitational Potential Energy.
Gravitational potential energy can be defined as

As M=m, then

Where,
m = Mass
G =Gravitational Universal Constant
R = Distance /Radius
PART A) As half its initial value is u'=2u, then



Therefore replacing we have that,

Re-arrange to find v,



Therefore the velocity when the separation has decreased to one-half its initial value is 816m/s
PART B) With a final separation distance of 2r, we have that

Therefore




Therefore the velocity when they are about to collide is 
Answer:
moment of inertia is 2.72 kg m²
Explanation:
given data
mass m = 10kg
height h = 4.5 m
radius r = 0.5 m
speed v = 6.5 m/s
to find out
moment of inertia
solution
we apply here conservation of energy
that is
mgh = 1/2 ×mv² + 1/2 × Iω²
here I is moment of inertia we find and
we know ω = Velocity / radius = 6.5 / 0.5 = 13
and g = 9.8
so put here all these value
10 (9.8) 4.5 = 1/2 ×(10)(6.5)² + 1/2 × I(13)²
441 = 211.25 + 1/2 × I( 169 )
I = 2.72
so moment of inertia is 2.72 kg m²
Answer:
720 J
Explanation:
The gravitational potential energy that Essam loses for every metre is given by:

where
m=72 kg is Essam's mass
is the gravitational field strength
is the difference in height
By substituting the numbers into the formula, we find

Explanation:
The inertia of a 4 kg mass is four times as great as a 1 kg mass.