Because sometimes it happens that they discover a dwarf planet
that nobody ever knew about before. When that happens, they
ADD the new one to the list of known dwarf planets, and then the
total number of dwarf planets on the list increases by 1 .
The change in velocity from 30 m/s north to 40 m/s south is a change of 70 m/s south
Answer:
Probability of tunneling is 
Solution:
As per the question:
Velocity of the tennis ball, v = 120 mph = 54 m/s
Mass of the tennis ball, m = 100 g = 0.1 kg
Thickness of the tennis ball, t = 2.0 mm = 
Max velocity of the tennis ball,
= 89 m/s
Now,
The maximum kinetic energy of the tennis ball is given by:

Kinetic energy of the tennis ball, KE' = 
Now, the distance the ball can penetrate to is given by:


Thus



Now,
We can calculate the tunneling probability as:



Taking log on both the sides:


To solve this problem we will use the concepts related to gravitational acceleration and centripetal acceleration. The equality between these two forces that maintains the balance will allow to determine how the rigid body is consistent with a spherically symmetric mass distribution of constant density. Let's start with the gravitational acceleration of the Star, which is

Here



Mass inside the orbit in terms of Volume and Density is

Where,
V = Volume
Density
Now considering the volume of the star as a Sphere we have

Replacing at the previous equation we have,

Now replacing the mass at the gravitational acceleration formula we have that


For a rotating star, the centripetal acceleration is caused by this gravitational acceleration. So centripetal acceleration of the star is

At the same time the general expression for the centripetal acceleration is

Where
is the orbital velocity
Using this expression in the left hand side of the equation we have that



Considering the constant values we have that


As the orbital velocity is proportional to the orbital radius, it shows the rigid body rotation of stars near the galactic center.
So the rigid-body rotation near the galactic center is consistent with a spherically symmetric mass distribution of constant density