The coordinates of a particle with respect to origin in a given reference frame is (1,1,1) meters. If a force of overrightarrowF=i-j+k acts on the particle, then the magnitude of torque (with respect to origin) in z-direction is ______.

Correct answer: 2. τ=overrightarrowr × overrightarrowF= | i j k 1 1 1 1 -1 1 | τ=k(-1-1)=-2 k |τ|=2 Nm

Q72 / 75 · JEE Main 2025 (29 Jan Shift 1) · Physics

The coordinates of a particle with respect to origin in a given reference frame is $(1,1,1)$ meters. If a force of $\overrightarrow{\mathrm{F}}=\hat{i}-\hat{j}+\hat{k}$ acts on the particle, then the magnitude of torque (with respect to origin) in z-direction is ______.

Correct answer: 2

Solution

$\begin{aligned} & \vec{\tau}=\overrightarrow{\mathrm{r}} \times \overrightarrow{\mathrm{F}}=\left|\begin{array}{ccc}\hat{\mathrm{i}} & \hat{\mathrm{j}} & \hat{\mathrm{k}} \\ 1 & 1 & 1 \\ 1 & -1 & 1\end{array}\right| \\ & \vec{\tau}=\hat{\mathrm{k}}(-1-1)=-2 \hat{\mathrm{k}} \\ & |\vec{\tau}|=2 \mathrm{Nm}\end{aligned}$

Hence, the correct answer is 2.

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The coordinates of a particle with respect to origin in a given reference frame is \((1,1,1)\) meters. If a force of \(\overrightarrow{\mathrm{F}}=\hat{i}-\hat{j}+\hat{k}\) acts on the particle, then the magnitude of torque (with respect to origin) in z-direction is ______.

Solution

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