The torque τ ? acts on a body about a given point is found to be equal to A ? * L ? where A ? is a constant nonzero vector and L ? is the angular momentum of the body about that point. Choose the incorrect option: ( A ? ≠ ± L ˆ )

The torque $\overset{?}{τ}$ acts on a body about a given point is found to be equal to $\overset{?}{A} * \overset{?}{L}$ where $\overset{?}{A}$ is a constant nonzero vector and $\overset{?}{L}$ is the angular momentum of the body about that point. Choose the incorrect option: $(\overset{?}{A} \neq \pm \hat{L})$

Option 1 - <math> <mrow> <mi mathvariant="normal"> </mi> </mrow> <mfrac> <mrow> <mrow> <mover accent="true"> <mrow> <mrow> <mi>d</mi> <mi>L</mi> </mrow> </mrow> <mo>⃗</mo> </mover> </mrow> </mrow> <mrow> <mrow> <mi>d</mi> <mi>t</mi> </mrow> </mrow> </mfrac> </math> is perpendicular to <math> <mover accent="true"> <mrow> <mrow> <mi>L</mi> </mrow> </mrow> <mo>⃗</mo> </mover> </math>  at all instants of time

Option 2 - The component of <math> <mover accent="true"> <mrow> <mrow> <mi>L</mi> </mrow> </mrow> <mo>⃗</mo> </mover> </math> in the direction of <math> <mover accent="true"> <mrow> <mrow> <mi>A</mi> </mrow> </mrow> <mo>⃗</mo> </mover> </math>  does not change with time

Option 3 - The magnitude of <math> <mover accent="true"> <mrow> <mrow> <mi>L</mi> </mrow> </mrow> <mo>⃗</mo> </mover> </math>  does not change with time

Option 4 -  <math> <mover accent="true"> <mrow> <mrow> <mi>L</mi> </mrow> </mrow> <mo>⃗</mo> </mover> </math> <img > does not change with time

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Raj Pandey | Contributor-Level 9

4 months ago

Correct Option - 3

Detailed Solution:

$\overset{?}{τ} = \frac{\overset{?}{d L}}{d t} = \overset{?}{A} * \overset{?}{L} \Rightarrow \frac{\overset{?}{d L}}{d t} ⊥ \overset{?}{L}$