Final answer:
Box 1 must weigh 51N, the same as box 2, in order to maintain the static equilibrium of the frictionless and weightless pulley system.
option A) 51N.
Step-by-step explanation:
When two boxes are connected in a pulley system and one weighs 51N, the system is in static equilibrium. In such a frictionless and weightless pulley scenario with strings and knots being negligible, the tensions in the strings must be equal because there is no acceleration and the system is at rest.
Since box 2 weighs 51N, the weight of box 1 must also be 51N to maintain equilibrium. According to Newton's first law of motion, the forces in the system need to be balanced for the objects to remain in a state of constant velocity (which includes being at rest).
In the given system, box 2 weighs 51N. To determine the weight of box 1, we can apply the principle of conservation of energy. Since box 1 and box 2 are connected by a pulley and neglecting friction, the tension in the string connecting the boxes is the same. Therefore, the weight of box 1 is also 51N, which corresponds to