Explanation:
We need to calculate the speed of light in each materials
(I). Gallium phosphide,
The index of refraction of Gallium phosphide is 3.50
Using formula of speed of light
....(I)
Where,
= index of refraction
c = speed of light
Put the value into the formula


(II) Carbon disulfide,
The index of refraction of Gallium phosphide is 1.63
Put the value in the equation (I)


(III). Benzene,
The index of refraction of Gallium phosphide is 1.50
Put the value in the equation (I)


Hence, This is the required solution.
Answer:
d= 7.32 mm
Explanation:
Given that
E= 110 GPa
σ = 240 MPa
P= 6640 N
L= 370 mm
ΔL = 0.53
Area A= πr²
We know that elongation due to load given as



A= 42.14 mm²
πr² = 42.14 mm²
r=3.66 mm
diameter ,d= 2r
d= 7.32 mm
For this case you must first know the definition of density.
D = m / v
where,
m: mass
v: volume.
You can then write the following hypothesis:
IF you know two physical characteristics of an object then you can determine the density. First weigh the object, THEN measure its volume BECAUSE the density is the quotient between the mass and the volume of an object.
A. 
The orbital speed of the clumps of matter around the black hole is equal to the ratio between the circumference of the orbit and the period of revolution:

where we have:
is the orbital speed
r is the orbital radius
is the orbital period
Solving for r, we find the distance of the clumps of matter from the centre of the black hole:

B. 
The gravitational force between the black hole and the clumps of matter provides the centripetal force that keeps the matter in circular motion:

where
m is the mass of the clumps of matter
G is the gravitational constant
M is the mass of the black hole
Solving the formula for M, we find the mass of the black hole:

and considering the value of the solar mass

the mass of the black hole as a multiple of our sun's mass is

C. 
The radius of the event horizon is equal to the Schwarzschild radius of the black hole, which is given by

where M is the mass of the black hole and c is the speed of light.
Substituting numbers into the formula, we find
