Question

The orbital speed of a satellite revolving around a planet in a circular orbit is ${v_o}$​. if its speed is increased by 10%, then
A) It will escape from its orbit
B) It will start rotating in an elliptical orbit
C) It will continue to move in the same orbit
D) It will move in a circular orbit of radius 20%more than radius of initial orbit.

Answer 1

Hint: To solve this question we have to know the basic thing is centripetal force is equals to gravitational force when it moves in a circular path, so we have to write those formula from that we got how the speed and radius of the orbit relates.

Complete answer:
As in the question mentioned the orbit speed of a satellite revolving around a planet in a circular path, so the Centripetal force is equal to gravitational force write it in a mathematical form.
$\dfrac{{m{v_0}^2}}{r} = \dfrac{{GmM}}{{{r^2}}}$
m and M is the mass of the object
v is the velocity of the object
r is the radius.
G is the universal gravitational constant which has value $6.674 \times {10^{ - 11}}{m^3}k{g^{ - 1}}{s^{ - 2}}$
The Centripetal force is the force defined as an object moving along the axis of rotation of a curved path and this force always acts towards the center.
The gravitational force also known as Newton's Law of Gravitation which states that in simple words the magnitude of the force between any two objects.
From the above relation we can conclude that
The centripetal force balancing the gravitational force on the satellite is directly proportional to the velocity and inversely proportional to the radius of the orbit.
As mentioned in the formulas. From that we can say
If the velocity increases the centripetal force will also increase and to counter that, the radius of the orbit should decrease as per the formula. Another way we can keep the radius unaltered in the equation is that the centripetal force will increase more than the gravitational force and the satellite will escape.

Hence the option A is the correct answer.

Note:
In this type of question we have to remember when the satellite has the circular path and elliptical path, so we can easily solve these types of questions. The question mentioned circular paths, so we take gravitational force as equals to centripetal force.