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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MCQ
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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

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

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

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

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

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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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