Rotational Motion

JEE Main level, numerical answer, medium

106 of 280

Question 106 of 280

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 ______.

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Answer: 2

τ⃗=r→×F→=∣i^j^k^1111−11∣τ⃗=k^(−1−1)=−2k^∣τ⃗∣=2Nm\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}

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