Question

A satellite is revolving around earth in a circular orbit at a uniform speed $v$. If gravitational force suddenly disappears speed of the satellite will be
A. Zero
B. V
C. Vc
D. Infinity

Answer 1

Hint: When any object is in circular motion, the centripetal force keeps an object moving in its circular path. This force always acts perpendicular to the object attracting it towards the centre of the circle. If we remove this force suddenly at a point of time the object loses its attraction towards the centre of the circle and at the same time it is not acted upon by any other force thus the object keeps moving in the direction in which its velocity vector is pointed.

Complete answer:
The satellite is revolving around the earth at a constant speed (with a speed of $V = \sqrt {\dfrac{{GM}}{R}} $where $M$ is the mass of earth and $R$ is the radius of circulation) and the gravitational pull from the earth is providing the centripetal force to the satellite which helps the satellite to move in the circle. Since this is a centripetal force, it has no effect on the magnitude of the speed, as it acts at right angle to the direction of motion.

Let’s consider an example of a ball tied to a string and is rotated, the tension in the string acts as a centripetal force. If the string is released then there will be no tension (i.e., centripetal force) of the string, the ball moves in a straight-line tangent to the circle of rotation.

So, if the gravitational force (which acts as a centripetal force to the satellite) disappears then the satellite will still move with the same speed in a straight-line tangent to the circle of revolution.Thus, the speed remains ‘V’ (unchanged) as the force acts at right angle to the direction of motion.

Therefore option B is correct.

Note: Even if the motion of the satellite is not circular (i.e., elliptical, parabolic or hyperbolic) the satellite will still move in a straight-line path in that direction in which its velocity is pointing at that particular moment. At any point of its trajectory the satellite is always acted upon by gravitational force which attracts the satellite towards the earth, satellites that revolve around the earth for broadcasting moves on this principle.