A 1 kg block subjected to two simultaneous forces and is moved a distance of 25 m along direction. The work done in this process is

Question

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. [2026]

Smart Achievers · Accepted Answer

(35)

$\begin{matrix} {\vec{F}}_{1} = (2 \hat{i} + 3 \hat{j} + 4 \hat{k}) N \\ {\vec{F}}_{2} = (3 \hat{i} - \hat{j} - 2 \hat{k}) N \end{matrix}} \Rightarrow {\vec{F}}_{net} = (5 \hat{i} + 2 \hat{j} + 2 \hat{k}) N$

$(distance) d = 25 m along (3 \hat{i} - 4 \hat{j}) direction$

$∴$ $displacement \vec{d} = 25 (\frac{3 \hat{i} - 4 \hat{j}}{\sqrt{9 + 16}}) = 25 (\frac{3 \hat{i} - 4 \hat{j}}{5}) m$

$\vec{d} = (15 \hat{i} - 20 \hat{j}) m$

$So, work done W = {\vec{F}}_{net} \cdot \vec{d}$

$W = (5 \hat{i} + 2 \hat{j} + 2 \hat{k}) \cdot (15 \hat{i} - 20 \hat{j}) = 35 J$

Solution

Q.
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. [2026]

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Solution

Q. A 1 kg block subjected to two simultaneous forces (2i^+3j^+4k^) N and (3i^-j^-2k^) N is moved a distance of 25 m along (3i^-4j^) direction. The work done in this process is _______ J. [2026]

Ans. (35) F→1=(2i^+3j^+4k^) NF→2=(3i^-j^-2k^) N}⇒F→net=(5i^+2j^+2k^) N (distance) d=25 m along (3i^-4j^) direction ∴ displacement d→=25(3i^-4j^9+16)=25(3i^-4j^5) m d→=(15i^-20j^) m So, work done W=F→net·d→ W=(5i^+2j^+2k^)·(15i^-20j^)=35 J

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Q.
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. [2026]