(C) The torque $\vec{\tau}$ is given by the cross product of the position vector $\vec{r}$ and the force vector $\vec{F}$:$\vec{\tau} = \vec{r} \times

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$-17 \hat{i} + 19 \hat{j} - 4 \hat{k}$

(C) The torque $\vec{\tau}$ is given by the cross product of the position vector $\vec{r}$ and the force vector $\vec{F}$:$\vec{\tau} = \vec{r} \times \vec{F}$Using the determinant form for the cross product:$\vec{\tau} = \begin{vmatrix} \hat{i} & \hat{j} & \hat{k} \\ 2 & 2 & 1 \\ 5 & 3 & -7 \end{vmatrix}$Expanding the determinant:$\vec{\tau} = \hat{i} [(2)(-7) - (1)(3)] - \hat{j} [(2)(-7) - (1)(5)] + \hat{k} [(2)(3) - (2)(5)]$$\vec{\tau} = \hat{i} [-14 - 3] - \hat{j} [-14 - 5] + \hat{k} [6 - 10]$$\vec{\tau} = -17 \hat{i} + 19 \hat{j} - 4 \hat{k}$

Class 11 Physics System of Particles and Rotational Motion Torque and Couple

Easy

The torque of a force $\vec{F} = 5 \hat{i} + 3 \hat{j} - 7 \hat{k}$ about the origin is $\vec{\tau}$. If the force acts on a particle whose position vector is $\vec{r} = 2 \hat{i} + 2 \hat{j} + \hat{k}$,then the value of $\vec{\tau}$ will be:

JEE MAIN 2022 All JEE MAIN

A
$11 \hat{i} + 19 \hat{j} - 4 \hat{k}$
B
$-11 \hat{i} + 9 \hat{j} - 16 \hat{k}$
C
$-17 \hat{i} + 19 \hat{j} - 4 \hat{k}$
D
$17 \hat{i} + 9 \hat{j} + 16 \hat{k}$

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System of Particles and Rotational Motion

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Torque and Couple

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Find the torque of a force $\vec{F} = -3\hat{i} + \hat{j} + 5\hat{k}$ acting at the point $\vec{r} = 7\hat{i} + 3\hat{j} + \hat{k}$.

MediumAIPMT 1997

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$A$ uniform cube of side $a$ and mass $m$ rests on a rough horizontal table. $A$ horizontal force $F$ is applied normal to one of the faces at a point that is directly above the centre of the face,at a height $\frac{3a}{4}$ above the base. The minimum value of $F$ for which the cube begins to tilt about the edge is (assume that the cube does not slide):

Medium

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The center of an equilateral triangle $ABC$ is $O$. Three forces $F_1$,$F_2$,and $F_3$ are applied along the sides $AB$,$BC$,and $AC$ respectively. If the total torque about $O$ is zero,what is the relationship between $F_1$,$F_2$,and $F_3$?

Easy

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Let $\vec{F}$ be a force acting on a particle having position vector $\vec{r}$,and $\vec{\tau}$ be the torque of this force about the origin. Then:

Medium

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Four forces are applied to a wheel of radius $10\,cm$ as shown in the figure. The net torque produced by all these forces about $C$ is

Difficult

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The torque of a force $\vec{F} = 5 \hat{i} + 3 \hat{j} - 7 \hat{k}$ about the origin is $\vec{\tau}$. If the force acts on a particle whose position vector is $\vec{r} = 2 \hat{i} + 2 \hat{j} + \hat{k}$,then the value of $\vec{\tau}$ will be:

Similar Questions

Find the torque of a force $\vec{F} = -3\hat{i} + \hat{j} + 5\hat{k}$ acting at the point $\vec{r} = 7\hat{i} + 3\hat{j} + \hat{k}$.

The center of an equilateral triangle $ABC$ is $O$. Three forces $F_1$,$F_2$,and $F_3$ are applied along the sides $AB$,$BC$,and $AC$ respectively. If the total torque about $O$ is zero,what is the relationship between $F_1$,$F_2$,and $F_3$?

Let $\vec{F}$ be a force acting on a particle having position vector $\vec{r}$,and $\vec{\tau}$ be the torque of this force about the origin. Then:

Four forces are applied to a wheel of radius $10\,cm$ as shown in the figure. The net torque produced by all these forces about $C$ is

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