JEE Mains · Physics · STD 11 - 6. system of particles and rotational motion
The torque due to the force \((2 \hat{i}+\hat{j}+2 \hat{k})\) about the origin, acting on a particle whose position vector is \((\hat{i}+\hat{j}+\hat{k})\), would be
- A \(\hat{i}-\hat{k}\)
- B \(\hat{i}+\hat{k}\)
- C \(\hat{j}+\hat{k}\)
- D \(\hat{i}-\hat{j}+\hat{k}\)
Answer & Solution
Correct Answer
(A) \(\hat{i}-\hat{k}\)
Step-by-step Solution
Detailed explanation
\(\begin{aligned} \tau & =\dot{r} \times \dot{F} \\ \tau & =\left|\begin{array}{lll}\hat{i} & \hat{j} & \hat{k} \\ 1 & 1 & 1 \\ 2 & 1 & 2\end{array}\right| \\ \tau & =\hat{i}(2-1)-\hat{j}[0]+\hat{k}(1-2) \\ & =\hat{i}-\hat{k}\end{aligned}\)
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