Question

A satellite orbiting Earth at an orbital radius r has a velocity v. Which represents the velocity if the satellite is moved to an orbital radius of 5r?
A.15√v


B.15v


C.5√v


D.5v

A. IS THE CORRECT ANSWER!

Answer 1

Answer:

The correct answer is V√5

Explanation:

Let V be the velocity of the satellite orbiting at radius r.

Let V(5r) be the velocity of the satellite orbiting at radius 5r.

Recall:

Escape velocity is given by:

V = √(2gr)

Where V is the escape velocity

g is the acceleration due to gravity

r is the radius of the earth.

With the above equation, we can obtain the answer to the question as follow:

V = √(2gr)

V(5r) = √(2g5r)

Next, we'll obtained the ratio of V(5r) to V as shown below

V(5r) : V => V(5r)/V

V(5r)/V = √(2g5r) / √(2gr)

V(5r)/V = √5

Cross multiply

V(5r) = V√5

From the above illustration, we can see that when the satellite is moved to 3r, then the expression for the velocity will be V√5