Part 1
If water does not spill at the top point of the circular motion then for the minimum speed condition we can say normal force will be zero at the top position



given that
R = 1 m
g = 9.8 m/s^2
now from above equation we have

Part b)
for minimum value of angular speed we will have



Answer:

Explanation:
Since the system is in international space station
so here we can say that net force on the system is zero here
so Force by the astronaut on the space station = Force due to space station on boy
so here we know that
mass of boy = 70 kg
acceleration of boy = 
now we know that


now for the space station will be same as above force




Answer:
a. a black hole
Explanation:
X-ray emission from the central degrees of the Milky Way Bright X-ray emission traces the coherent edge brightened shell-like feature, dubbed the northern chimney, located north of Sgr A* and characterized by a diameter of about 160 pc. On the opposite side, the southern chimney appears as a bright linear feature. Bright X-ray emission is observed at high latitude
Answer:
a) 
b) 
c) 
d)
would be the same.
would decrease.
would be the same.
Explanation:
a) On an inclined plane the force of gravity is the sine component of the weight of the block.

b) The friction force is equal to the normal force times coefficient of friction.

c) The work done by the normal force is zero, since there is no motion in the direction of the normal force.
d) The relation between the vertical height and the distance on the ramp is

According to this relation, the work done by the gravity wouldn't change, since the force of gravity includes a term of
.
The work done by the friction force would decrease, because both the cosine term and the distance on the ramp would decline.
The work done by the normal force would still be zero.