JEE Main 2026 — Apr 4, Shift 1 — Physics solution

JEE Main2026Apr 4, Shift 1Physics

A $1$ kg block subjected to two simultaneous forces $(2 \hat{i} + 3 \hat{j} + 4 \hat{k})$ N and $(3 \hat{i} - \hat{j} - 2 \hat{k})$ N is moved a distance of $25$ m along $(3 \hat{i} - 4 \hat{j})$ direction. The work done in this process is ________ J.

Your answer

Solution

Net force: $F = (2 + 3) \hat{i} + (3 - 1) \hat{j} + (4 - 2) \hat{k} = 5 \hat{i} + 2 \hat{j} + 2 \hat{k}$ N.

Displacement: unit vector along $(3 \hat{i} - 4 \hat{j})$ has magnitude $5$ , so $\overset{n}{^} = \frac{3 i ^ - 4 j ^}{5}$ and $S = 25 \overset{n}{^} = 15 \hat{i} - 20 \hat{j}$ m.

$W = F \cdot S = 5 (15) + 2 (- 20) + 2 (0) = 75 - 40 = 35$ J.

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