Final answer:
The frictional force at the base of sphere A is zero because the sphere is in equilibrium and there is no other horizontal force to balance the applied force, implying any friction at the base must be nil. For a mass m = 500 g, the normal reaction at the base of A is 19.6 N, calculated by balancing the object's weight.
Step-by-step explanation:
To show that the magnitude of the frictional force at the base of sphere A is zero, consider that the system is in equilibrium. This means that the net force and net torque acting on each sphere must be zero. Starting with sphere A, the horizontal force of magnitude 2mg is applied at the top, and since there's no acceleration, this must be balanced by other forces in the system. The only horizontal force that can balance this is the frictional force at the point of contact between sphere A and B. However, since this force must also be balanced by an equal and opposite force and no other horizontal forces are present, it implies that the frictional force at the base of A must indeed be zero.
Now, considering the normal reaction at the base of sphere A, it must balance the weight of sphere A. It acts vertically upwards, while the weight acts vertically downwards. The mass of sphere A is given as 4m, so its weight is 4mg. Therefore, the normal reaction at the base of sphere A is also 4mg to support it against gravity's pull. With m=500 g, or 0.5 kg, the magnitude of the normal reaction at the base of A will be 4 * 0.5 kg * 9.8 m/s2, which is 19.6 N.