# Let → F Be a Force Acting on a Particle Having Position Vector → R . Let → γ Be the Torque of this Force About the Origin, Then - Physics

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Let $\overrightarrow F$ be a force acting on a particle having position vector $\overrightarrow r.$ Let $\overrightarrow\Gamma$ be the torque of this force about the origin, then __________ .

#### Options

• $\overrightarrow{r} . \overrightarrow{\Gamma} = 0\text{ and }\overrightarrow{F} . \overrightarrow{\Gamma} = 0$

• $\overrightarrow{r} . \overrightarrow{\Gamma} = 0\text{ but }\overrightarrow{F} . \overrightarrow{\Gamma} \ne 0$

• $\overrightarrow{r} . \overrightarrow{\Gamma} \ne 0\text{ but }\overrightarrow{F} . \overrightarrow{\Gamma} = 0$

• $\overrightarrow{r} . \overrightarrow{\Gamma} \ne 0\text{ and }\overrightarrow{F} . \overrightarrow{\Gamma} \ne 0$

#### Solution

$\overrightarrow{r} . \overrightarrow{\Gamma} = 0\text{ and }\overrightarrow{F} . \overrightarrow{\Gamma} = 0$

We have

$\overrightarrow{\Gamma} = \overrightarrow{r} \times \overrightarrow{F}$

Thus,

$\overrightarrow{\Gamma}$ is perpendicular to $\overrightarrow{r}$ and $\overrightarrow{F}.$

Therefore, we have

$\overrightarrow{r} . \overrightarrow{\Gamma} = 0\text{ and }\overrightarrow{F} . \overrightarrow{\Gamma} = 0$

Is there an error in this question or solution?
Chapter 10: Rotational Mechanics - MCQ [Page 193]

#### APPEARS IN

HC Verma Class 11, Class 12 Concepts of Physics Vol. 1
Chapter 10 Rotational Mechanics
MCQ | Q 8 | Page 193
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