A particle falls towards Earth from infinity. Its velocity on reaching the Earth would be

Explanation

The velocity acquired by a particle falling towards Earth from infinity (assuming no initial velocity) can be calculated using the equation for gravitational potential energy. The velocity when reaching Earth's surface is given by v^2=2gh , where g is the acceleration due to gravity and ℎh is the height from which the particle falls. Since the particle falls from infinity, ℎh is effectively infinite, and the velocity becomes (2gR )^1/2.Incorrect Options Explanation:a) gR (Incorrect): This value does not represent the final velocity of the particle. While the force driving the fall is g, additional factors like initial velocity and distance traveled contribute to the final velocity.(b) 2 g/R (Incorrect): While the answer involves g and R, it is not the final velocity. Additionally, the square root sign is not typically used in this context of reaching escape velocity.(c) g/R (Incorrect): this doesn't corresponds to the correct value.