I believe that it is the first one just a guess tho. So don't trust me, just in case
Answer:
∆T = Mv^2Y/2Cp
Explanation:
Formula for Kinetic energy of the vessel = 1/2mv^2
Increase in internal energy Δu = nCVΔT
where n is the number of moles of the gas in vessel.
When the vessel is to stop suddenly, its kinetic energy will be used to increase the temperature of the gas
We say
1/2mv^2 = ∆u
1/2mv^2 = nCv∆T
Since n = m/M
1/2mv^2 = mCv∆T/M
Making ∆T subject of the formula we have
∆T = Mv^2/2Cv
Multiple the RHS by Cp/Cp
∆T = Mv^2/2Cv *Cp/Cp
Since Y = Cp/CV
∆T = Mv^2Y/2Cp k
Since CV = R/Y - 1
We could also have
∆T = Mv^2(Y - 1)/2R k
Explanation:
We have,
Semimajor axis is 
It is required to find the orbital period of a dwarf planet. Let T is time period. The relation between the time period and the semi major axis is given by Kepler's third law. Its mathematical form is given by :

G is universal gravitational constant
M is solar mass
Plugging all the values,

Since,

So, the orbital period of a dwarf planet is 138.52 years.
Answer:
0.301 m
Explanation:
Torque = Force × Radius
τ = Fr
40.0 Nm = 133 N × r
r = 0.301 m
The mechanic must apply the force 0.301 m from the nut.
To solve this problem it is necessary to apply the definition of severity of Newtonian laws in which it is specified that gravity is defined by

Where
G= Gravitational Constant
M = Mass of Earth
R= Radius from center of the planet
According to the information we need to find the gravity 350km more than the radius of Earth, then



Therefore the gravitational acceleration at 350km is 