Final Answer:
The correct answer is 2.450 J, thus the correct option is C.
Explanation:
The given problem can be solved using the Law of Conservation of Mechanical Energy. This law states that the total mechanical energy of an object remains constant during its motion. Therefore, the total mechanical energy of the 2.5kg solid sphere at the top of the ramp is equal to the total mechanical energy of the sphere at the bottom of the ramp. The total mechanical energy at the top of the ramp is equal to the potential energy of the sphere. The potential energy of the sphere is given by the formula U = mgh, where m is the mass of the sphere, g is the acceleration due to gravity and h is the height of the ramp. Substituting the given values into the formula, we get U = 2.5 x 9.8 x 0.1 = 2.45 J. The total mechanical energy of the sphere at the bottom of the ramp is equal to the kinetic energy of the sphere. The kinetic energy of the sphere is given by the formula K = ½mv2, where m is the mass of the sphere and v is the velocity of the sphere. Since the sphere is released from rest, the velocity at the bottom of the ramp is 0 and therefore the kinetic energy of the sphere at the bottom of the ramp is 0. Hence, the total mechanical energy of the sphere at the top of the ramp is equal to the total mechanical energy of the sphere at the bottom of the ramp, i.e. 2.45 J. Therefore, option c) 2.450 J is the correct answer.