UPSC NDA 2 2021 General Ability Solved Paper

Concept:Work is defined as the dot product of force and displacement.$W = \vec{F} \cdot \vec{s} = Fs\cos\theta$.When force and displacement are in the same direction, $W = Fs$.SI unit: $1$ Joule $= 1$ Newton $\times 1$ metre.Thus, $1\ \text{J}$ is the work done when a force of $1\ \text{N}$ moves an object $1\ \text{m}$ in its direction.Explanation:Check each option using $W = F \times s$.Option A: Force $F = 4\ \text{N}$, displacement $s = 25\ \text{cm} = 0.25\ \text{m}$.$W = 4 \times 0.25 = 1\ \text{J}$.Option B: $F = 2\ \text{N}$, $s = 1\ \text{m} \Rightarrow W = 2 \times 1 = 2\ \text{J}$.Option C: $F = 1\ \text{N}$, $s = 1\ \text{cm} = 0.01\ \text{m} \Rightarrow W = 0.01\ \text{J}$.Option D: $F = 1\ \text{N}$, $s = 50\ \text{cm} = 0.5\ \text{m} \Rightarrow W = 0.5\ \text{J}$.Only option A gives exactly $1$ Joule.Answer:Option A: $4\ \text{N}$ moves an object by $25\ \text{cm}$.