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

Physics · Rotational Dynamics

JEE Main 2025 — 29 January, Morning Shift — Question 40

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

Answer: 2

Numerical answer — enter this value.

Step-by-step solution

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

$\vec{\tau}=\hat{\mathrm{k}}(-1-1)=-2 \hat{\mathrm{k}}$ $|\vec{\tau}|=2 \mathrm{Nm}$

Answer key and solution verified before publishing.

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Exam: JEE Main 2025
Paper: 29 January, Morning Shift
Subject: Physics
Chapter: Rotational Dynamics
Topic: Torque, Equation of Motion and Toppling