How would the speed of earth’s orbit around the sun change if earth’s distance from the sun increased by 4 times?
a. it would increase by a factor of 2.
b. it would increase by a factor of 4.
c. it would decrease by a factor of 2.
d. the speed would not change.

c. it would decrease by a factor of 2.

Explanation:

As we know that centripetal force on Earth due to Sun is due to gravitational attraction force of Sun

Now we will have

now we have

now if the orbital radius or the distance from sun is increased by factor of 4

so the orbital speed is changed by

so the speed would be given as

so it is half of the initial speed

speed of light in vacuum is 300,000 km/s

speed of light in other mediums is given by the expression v = c/n, where c is the speed of light in vacuum and n is the refractive index of medium.

for the first medium v = 200,000 km/s

  so, refractive index of medium = 300000/200000 = 1.5

    1.5 refractive index is usually for glass. so first medium is glass.

for the second medium v = 250,00 km/s

so, refractive index of medium = 300000/250000 = 1.2

    1.2 refractive index is usually for water. so second medium is water.

for the third medium v = 0 km/s

so, refractive index of medium = 300000/0 = ∞

    ∞ refractive index is usually for opaque mediums. so third medium is opaque medium.