Explanation:
It is given that,
A planet were discovered between the sun and Mercury, with a circular orbit of radius equal to 2/3 of the average orbit radius of Mercury.
Mass of the Sun, 
Radius of Mercury's orbit, 
Radius of discovered planet, 

Let T is the orbital period of such a planet. Using Kepler's third law of planetary motion as :




T = 4135214.625 s
or
T = 47.86 days
So, the orbital period of such a planet is 47.86 days. Hence, this is the required solution.
Answer:
Energy due to air resistance = 31.8 Joules
Explanation:
According to the law of conservation of energy, energy can neither be created nor destroyed but can be transformed from one form to another
Kinetic Energy + Energy due to air resistance = Potential energy..........(1)
If there is no energy loss due to air resistance, potential energy = kinetic energy
mass, m = 1.5 kg
height, h = 4.0 m
speed, v = 6 m/s
Kinetic energy = 0.5 mv²
Kinetic energy = 0.5 * 1.5 * 6²
Kinetic energy = 27 Joules
Potential Energy = mgh
Potential energy = 1.5 * 9.8 * 4
Potential energy = 58.8 Joules
From equation (1)
27 + Energy due to air resistance = 58.8
Energy due to air resistance = 58.8 - 27
Energy due to air resistance = 31.8 Joules
Speed of wave = Frequency x Wavelength
so Speed = 0.7 x 9 = 6.3
remember the calculations must be done in their Basic SI units.
therefore, you have to convert 7 mm to meters which becomes 0.7 meters
Answer:
The mass rate of the cooling water required is: 
Explanation:
First, write the energy balance for the condensator: The energy that enters to the equipment is the same that goes out from it; consider that there is no heat transfer to the surroundings and kinetic and potential energy changes are despreciable.

Where w refers to the cooling water and s to the steam flow. Reorganizing,

Write the difference of enthalpy for water as Cp (Tout-Tin):

This equation will let us to calculate the mass rate required. Now, let's get the enthalpy and Cp data. The enthalpies can be read from the steam tables (I attach the tables I used). According to that,
and
can be calculated as:
.
The Cp of water at 25ºC (which is the expected average temperature for water) is: 4.176
. If the average temperature is actually different, it won't mean a considerable mistake. Also we know that
, so let's work with the limit case, which is
to calculate the minimum cooling water mass rate required (A higher one will give a lower temperature difference as a result). Finally, replace data:
