A satellite of the earth is revolving in a circular orbit with a uniform speed \(\mathrm{v} .\) If the gravitational force suddenly disappears, the satellite will (A) Continue to move with velocity \(\mathrm{v}\) along the original orbit. (B) Move with a Velocity \(\mathrm{v}\), tangentially to the original orbit. (C) Fall down with increasing velocity. (D) Ultimately come to rest somewhere on the original orbit.

Gravitational force is the centripetal force that keeps a satellite in its circular orbit around the Earth. The gravitational force acts towards the center of the Earth, pulling the satellite and preventing it from moving in a straight line due to its inertia.

If the gravitational force suddenly disappears, there would no longer be a centripetal force acting on the satellite. In this situation, the satellite would continue to move in the direction of its current velocity due to its inertia.

(A) This choice states that the satellite will continue to move with velocity v along the original orbit. However, this is incorrect as there's no force that will keep it in its circular orbit once the gravitational force disappears. (B) This choice states that the satellite will move with a velocity v, tangentially to the original orbit. This is the correct answer because, in the absence of the gravitational force, the satellite will move in a straight line due to its inertia, which means that it will move tangentially to the original orbit at the instant when the gravitational force disappears. (C) This choice states that the satellite will fall down with increasing velocity. This is incorrect because there is no force acting on the satellite to cause this acceleration or change in direction. (D) This choice states that the satellite will ultimately come to rest somewhere on the original orbit. This is incorrect because there is no force acting to decelerate the satellite eventually. Based on our analysis, the correct answer is (B): Move with a Velocity \(\mathrm{v}\), tangentially to the original orbit.