Torque acting on the body is:

Q: Torque acting on the body is:

The correct option is (2): $\vec{r}\times\vec{F}$ Torque, often denoted by $\vec{\tau}$ (tau), is the rotational equivalent of linear force. Just as a force causes an object to accelerate linearly, a torque causes an object to undergo angular acceleration, leading to rotation. In physics, torque is formally defined as the cross product of the position vector ($\vec{r}$) from the pivot point to the point where the force is applied, and the force vector ($\vec{F}$) itself. This relationship is expressed as $\vec{\tau} = \vec{r}\times\vec{F}$. The magnitude of the torque is given by $\tau = rF\sin\theta$, where $\theta$ is the angle between $\vec{r}$ and $\vec{F}$. The direction of the torque is perpendicular to both $\vec{r}$ and $\vec{F}$, following the right-hand rule. This definition is fundamental in rotational dynamics and is crucial for understanding how forces induce rotational motion in extended bodies. The incorrect option is (1): $\vec{r}\times\vec{p}$ This expression represents the angular momentum of a particle, not torque. Angular momentum ($\vec{L}$) is the cross product of the position vector ($\vec{r}$) and the linear momentum ($\vec{p}$), i.e., $\vec{L} = \vec{r}\times\vec{p}$. The incorrect option is (3): $\vec{p}\times\vec{r}$ This is the negative of angular momentum ($\vec{L}$). The order of vectors in a cross product matters, as $\vec{A}\times\vec{B} = -\vec{B}\times\vec{A}$. Therefore, $\vec{p}\times\vec{r} = -\vec{L}$, and it does not represent torque. The incorrect option is (4): $\vec{F}\times\vec{r}$ This expression is incorrect because, while it involves the force and position vectors, the order of the cross product is reversed compared to the standard definition of torque. Torque is defined as $\vec{r}\times\vec{F}$, and reversing the order gives a vector in the opposite direction ($\vec{F}\times\vec{r} = -\vec{\tau}$).

Question

Accepted Answer

The correct option is (2): $\vec{r}	imes\vec{F}$

Torque, often denoted by $\vec{	au}$ (tau), is the rotational equivalent of linear force. Just as a force causes an object to accelerate linearly, a torque causes an object to undergo angular acceleration, leading to rotation. In physics, torque is formally defined as the cross product of the position vector ($\vec{r}$) from the pivot point to the point where the force is applied, and the force vector ($\vec{F}$) itself. This relationship is expressed as $\vec{	au} = \vec{r}	imes\vec{F}$. The magnitude of the torque is given by $	au = rF\sin	heta$, where $	heta$ is the angle between $\vec{r}$ and $\vec{F}$. The direction of the torque is perpendicular to both $\vec{r}$ and $\vec{F}$, following the right-hand rule. This definition is fundamental in rotational dynamics and is crucial for understanding how forces induce rotational motion in extended bodies.

The incorrect option is (1): $\vec{r}	imes\vec{p}$
This expression represents the angular momentum of a particle, not torque. Angular momentum ($\vec{L}$) is the cross product of the position vector ($\vec{r}$) and the linear momentum ($\vec{p}$), i.e., $\vec{L} = \vec{r}	imes\vec{p}$.

The incorrect option is (3): $\vec{p}	imes\vec{r}$
This is the negative of angular momentum ($\vec{L}$). The order of vectors in a cross product matters, as $\vec{A}	imes\vec{B} = -\vec{B}	imes\vec{A}$. Therefore, $\vec{p}	imes\vec{r} = -\vec{L}$, and it does not represent torque.

The incorrect option is (4): $\vec{F}	imes\vec{r}$
This expression is incorrect because, while it involves the force and position vectors, the order of the cross product is reversed compared to the standard definition of torque. Torque is defined as $\vec{r}	imes\vec{F}$, and reversing the order gives a vector in the opposite direction ($\vec{F}	imes\vec{r} = -\vec{	au}$).