A particle located at the position vector $\hat { \mathbf { r } } = ( \tilde { \mathbf { i } } + \hat { \mathbf { j } } )$ m has a force $\overrightarrow { \mathbf { F } } = ( 2 \hat { \mathbf { i } } + 3 \tilde { \mathbf { j } } )$ N acting on it.The torque about the origin is
A)(1 )N.m
B)(5 )N.m
C)(-1 )N.m
D)(-5 )N.m
E)(2 $\hat { \mathbf { i } }$ + 3 $\hat { \mathbf {j} }$ )N.m

Question

A particle located at the position vector $\hat { \mathbf { r } } = ( \tilde { \mathbf { i } } + \hat { \mathbf { j } } )$ m has a force $\overrightarrow { \mathbf { F } } = ( 2 \hat { \mathbf { i } } + 3 \tilde { \mathbf { j } } )$ N acting on it.The torque about the origin is
A)(1 )N.m 
B)(5 )N.m 
C)(-1 )N.m 
D)(-5 )N.m 
E)(2 $\hat { \mathbf { i } }$ + 3 $\hat { \mathbf {j} }$ )N.m

Quizplus · Accepted Answer

The torque about the origin is given by $\overrightarrow { \mathbf { \tau } } = \overrightarrow { \mathbf { r } } \times \overrightarrow { \mathbf { F } } $. Substituting the given values, we get:$$\overrightarrow { \mathbf { \tau } } = \begin{pmatrix} \tilde { \mathbf { i } } + \hat { \mathbf { j } } \end{pmatrix} \times \begin{pmatrix} 2 \hat { \mathbf { i } } + 3 \tilde { \mathbf { j } } \end{pmatrix} = \begin{pmatrix} 3 \hat { \mathbf { k } } \end{pmatrix} \text{ Nm}$$Therefore, the torque about the origin is 3 Nm in the $\hat { \mathbf { k } }$ direction.

A Particle Located at the Position Vector r^=(i~+j^)\hat { \mathbf { r } } = ( \tilde { \mathbf { i } } + \hat { \mathbf { j } } )r^=(i~+j^​)

A Particle Located at the Position Vector $\hat { \mathbf { r } } = ( \tilde { \mathbf { i } } + \hat { \mathbf { j } } )$