Q70 / 75 · JEE Main 2025 (22 Jan Shift 2) · Physics

A force $\overrightarrow{\mathrm{F}}=2 \hat{i}+\mathrm{b} \hat{j}+\hat{k}$ is applied on a particle and it undergoes a displacement $\hat{i}-2 \hat{j}-\hat{k}$. What will be the value of $b$, if work done on the particle is zero.

  • A
    0
  • Correct answer
    B
    $\frac{1}{2}$
  • C
    2
  • D
    $\frac{1}{3}$

Solution

$\begin{aligned} & w=0 \\ & \therefore \quad \vec{F} \cdot S=0 \\ & (2 \hat{i}+b \hat{j}+\hat{k}) \cdot(\hat{i}-2 \hat{j}-\hat{k})=0 \\ & 2-2 b-1=0 \\ & b=\frac{1}{2}\end{aligned}$

Hence, the correct answer is option: 'B'.

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