Question

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

• A. $\overset{\rightarrow}{r}.\overset{\rightarrow}{T} = 0and\overset{\rightarrow}{F}.\overset{\rightarrow}{T} = 0$
• B. $\overset{\rightarrow}{r}.\overset{\rightarrow}{T} = 0and\overset{\rightarrow}{F}.\overset{\rightarrow}{T} \neq 0$
• C. $\overset{\rightarrow}{r}.\overset{\rightarrow}{T} \neq 0and\overset{\rightarrow}{F}.\overset{\rightarrow}{T} = 0$
• D. . $\overset{\rightarrow}{r}.\overset{\rightarrow}{T} \neq 0and\overset{\rightarrow}{F}.\overset{\rightarrow}{T} \neq 0$

Answer 1

Answer: (A)

$\overset{\rightarrow}{r}.\overset{\rightarrow}{T} = 0and\overset{\rightarrow}{F}.\overset{\rightarrow}{T} = 0$

Answer 2

$\overset{\rightarrow}{T} = \overset{\rightarrow}{r} \times \overset{\rightarrow}{F}$ is $\overset{\rightarrow}{T}$ to both $\overset{\rightarrow}{r}$ and $\overset{\rightarrow}{F}$ so $\overset{\rightarrow}{T}$ and $\overset{\rightarrow}{F}.\overset{\rightarrow}{T} = 0$