Final answer:
The work done by gravity during the upward motion of a projected particle is negative and corresponds to the loss in potential energy, given by the formula −mu²sin²θ/2. The Correct Answer is Option .A.
Step-by-step explanation:
The work done by gravity on a particle during its upward motion can be determined by the change in gravitational potential energy, which is the product of the mass (m), the acceleration due to gravity (g), and the change in height (h). The initial kinetic energy is projected into two components due to the angle: a horizontal component (ucosθ) and a vertical component (usinθ).
The work done by gravity against the vertical motion is negative, as gravity works in the opposite direction of the displacement. Therefore, the correct answer is A. −mu²sin²θ/2, because the work done by gravity is equal to the negative change in potential energy, which corresponds to the negative of the initial vertical component of kinetic energy.