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JEE Main 202522 JanuaryEvening Shift
Exam
JEE Main
Year
2025
Date
22 January
Shift
Evening Shift
Subject
Physics
Chapter
Rotational Motion

JEE Main 2025 · 22 January · Evening Shift · Physics · Rotational Motion

The torque due to the force (2 i + j +2 k ) about the origin,...

The torque due to the force (2i^+j^+2k^)(2 \hat{i}+\hat{j}+2 \hat{k}) about the origin, acting on a particle whose position vector is (i^+j^+k^)(\hat{i}+\hat{j}+\hat{k}), would be

Options

  1. Ai^−k^\hat{i}-\hat{k}
  2. Bi^+k^\hat{i}+\hat{k}
  3. Cj^+k^\hat{j}+\hat{k}
  4. Di^−j^+k^\hat{i}-\hat{j}+\hat{k}

Correct answer

A. i^−k^\hat{i}-\hat{k}

Step-by-step solution

τ=r˙×F˙τ=∣i^j^k^111212∣τ=i^(2−1)−j^[0]+k^(1−2)=i^−k^\begin{aligned} \tau & =\dot{r} \times \dot{F} \\ \tau & =\left|\begin{array}{lll}\hat{i} & \hat{j} & \hat{k} \\ 1 & 1 & 1 \\ 2 & 1 & 2\end{array}\right| \\ \tau & =\hat{i}(2-1)-\hat{j}[0]+\hat{k}(1-2) \\ & =\hat{i}-\hat{k}\end{aligned}
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