(C) The torque of a couple is given by the sum of the torques of the individual forces about the origin.$\vec{\tau} = (\vec{r_1} \times \vec{F_1}) + (

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(C) The torque of a couple is given by the sum of the torques of the individual forces about the origin.$\vec{\tau} = (\vec{r_1} \times \vec{F_1}) + (\vec{r_2} \times \vec{F_2})$Given $\vec{r_1} = 3\hat{i}$,$\vec{F_1} = 1\hat{j}$ and $\vec{r_2} = 3\hat{j}$,$\vec{F_2} = -1\hat{j}$.$\vec{\tau} = (3\hat{i} \times 1\hat{j}) + (3\hat{j} \times -1\hat{j})$Since $\hat{i} \times \hat{j} = \hat{k}$ and $\hat{j} \times \hat{j} = 0$,we get:$\vec{\tau} = 3\hat{k} + 0 = 3\hat{k} \ Nm$.

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

Medium

The position vectors of two particles of a rigid body are $(3, 0, 0) \ m$ and $(0, 3, 0) \ m$. Forces of $(0, 1, 0) \ N$ and $(0, -1, 0) \ N$ act on these particles respectively. The torque of the couple is ....... $Nm$.

A
Zero
B
$3\hat{k} - \hat{j}$
C
$3\hat{k}$
D
$3\hat{k} + \hat{j}$

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Class 11

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Chapter

System of Particles and Rotational Motion

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Torque and Couple

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

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$A$ door $1.2 \,m$ wide requires a force of $1 \,N$ to be applied perpendicularly at the free end to open or close it. The perpendicular force required at a point $0.2 \,m$ distant from the hinges for opening or closing the door is: (in $\,N$)

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Moment of a force of magnitude $20 \, N$ acting along the positive $x$-direction at point $(3 \, m, 0, 0)$ about the point $(0, 2, 0)$ (in $N \cdot m$) is ...........

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$A$ force of $(2\hat i - 4\hat j + 2\hat k) \ N$ acts at a point $(3\hat i + 2\hat j - 4\hat k) \ m$ from the origin. The magnitude of torque is ......... $N-m$.

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Why is the handle of a door or window placed at the end opposite to the hinged side?

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The position vectors of two particles of a rigid body are $(3, 0, 0) \ m$ and $(0, 3, 0) \ m$. Forces of $(0, 1, 0) \ N$ and $(0, -1, 0) \ N$ act on these particles respectively. The torque of the couple is ....... $Nm$.

Similar Questions

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

$A$ door $1.2 \,m$ wide requires a force of $1 \,N$ to be applied perpendicularly at the free end to open or close it. The perpendicular force required at a point $0.2 \,m$ distant from the hinges for opening or closing the door is: (in $\,N$)

Moment of a force of magnitude $20 \, N$ acting along the positive $x$-direction at point $(3 \, m, 0, 0)$ about the point $(0, 2, 0)$ (in $N \cdot m$) is ...........

$A$ force of $(2\hat i - 4\hat j + 2\hat k) \ N$ acts at a point $(3\hat i + 2\hat j - 4\hat k) \ m$ from the origin. The magnitude of torque is ......... $N-m$.

Why is the handle of a door or window placed at the end opposite to the hinged side?

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