The torque <math> <mover accent="true"> <mrow> <mrow> <mi>τ</mi> </mrow> </mrow> <mo>?</mo> </mover> </math> acts on a body about a given point is found to be equal to <math> <mover accent="true"> <mrow> <mrow> <mi>A</mi> </mrow> </mrow> <mo>?</mo> </mover> <mo>×</mo> <mover accent="true"> <mrow> <mrow> <mi>L</mi> </mrow> </mrow> <mo>?</mo> </mover> </math> where <math> <mover accent="true"> <mrow> <mrow> <mi>A</mi> </mrow> </mrow> <mo>?</mo> </mover> </math> is a constant nonzero vector and <math> <mover accent="true"> <mrow> <mrow> <mi>L</mi> </mrow> </mrow> <mo>?</mo> </mover> </math> is the angular momentum of the body about that point. Choose the incorrect option: <math> <mo>(</mo> <mover accent="true"> <mrow> <mrow> <mi>A</mi> </mrow> </mrow> <mo>?</mo> </mover> <mo>≠</mo> <mo>±</mo> <mover accent="true"> <mrow> <mrow> <mi>L</mi> </mrow> </mrow> <mi>&circ;</mi> </mover> <mo>)</mo> </math>

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Physics Class 11th Physics System of Particles and Rotational Motion

The torque $\overset{?}{τ}$ acts on a body about a given point is found to be equal to $\overset{?}{A} \times \overset{?}{L}$ 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 -

$\frac{\vec{d L}}{d t}$ is perpendicular to $\vec{L}$ at all instants of time

Option 2 -

The component of $\vec{L}$ in the direction of $\vec{A}$ does not change with time

Option 3 -

The magnitude of $\vec{L}$ does not change with time

Option 4 -

$\vec{L}$ does not change with time

2 Views | Posted a month ago

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1 Answer

Answered by

Raj Pandey | Contributor-Level 9

a month ago

Correct Option - 3

Detailed Solution:

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

$∴$ Statement (1) is correct

The component of $\overset{?}{L}$ in the direction of $\overset{?}{A}$ is always perpendicular to , so it does not change.

$∴$ Statement (2) is correct

The magnitude of $\overset{?}{L}$ does not change with time as $\overset{?}{τ} ⊥ \overset{?}{L}$ .

$∴$ Statement (3) is correct

The direction of $\overset{?}{L}$ changes with time.

$∴$ Statement (4) is incorrect.

<math> <mover accent="true"> <mrow> <mrow> <mi>τ</mi> </mrow> </mrow> <mo>? </mo> </mover> <mo>=</mo> <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> <mo>=</mo> <mover accent="true"> <mrow> <mrow> <mi>A</mi> </mrow> </mrow> <mo>? </mo> </mover> <mo>×</mo> <mover accent="true"> <mrow> <mrow> <mi>L</mi> </mrow> </mrow> <mo>? </mo> </mover> <mo>⇒</mo> <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> <mo>⊥</mo> <mover accent="true"> <mrow> <mrow> <mi>L</mi> </mrow> </mrow> <mo>? </mo> </mover> </math> <math> <mo>∴</mo> <mrow> <mi mathvariant="normal"> </mi> </mrow> </math> Statement (1) is correct<div><div><picture><source srcset="" media=" (max-width: 500px)"><img src="https://images.shiksha.com/mediadata/images/1757498222phpd7VEy0.jpeg" alt="" width="162" height="122" loading="lazy"></picture></div></div> The component of <math> <mover accent="true"> <mrow> <mrow> <mi>L</mi> </mrow> </mrow> <mo>? </mo> </mover> </math> <math><mover accent="true"><mrow><mrow></mrow></mrow></mover></math> in the direction of <math> <mover accent="true"> <mrow> <mrow> <mi>A</mi> </mrow> </mrow> <mo>? </mo> </mover> </math> <math><mover accent="true"><mrow><mrow></mrow></mrow></mover></math> is always perpendicular to <math><mover accent="true"><mrow><mrow></mrow></mrow></mover></math> , so it does not change.<math></math> <math> <mo>∴</mo> <mrow> <mi mathvariant="normal"> </mi> </mrow> </math>  Statement (2) is correctThe magnitude of <math> <mover accent="true"> <mrow> <mrow> <mi>L</mi> </mrow> </mrow> <mo>? </mo> </mover> </math> <math><mover accent="true"><mrow><mrow></mrow></mrow></mover></math> does not change with time as <math> <mover accent="true"> <mrow> <mrow> <mi>τ</mi> </mrow> </mrow> <mo>? </mo> </mover> <mo>⊥</mo> <mover accent="true"> <mrow> <mrow> <mi>L</mi> </mrow> </mrow> <mo>? </mo> </mover> </math> <math><mover accent="true"><mrow><mrow></mrow></mrow></mover><mover accent="true"><mrow><mrow></mrow></mrow></mover></math> .<math></math> <math> <mo>∴</mo> <mrow> <mi mathvariant="normal"> </mi> </mrow> </math>  Statement (3) is correctThe direction of <math><mover accent="true"><mrow><mrow></mrow></mrow></mover></math> <math> <mover accent="true"> <mrow> <mrow> <mi>L</mi> </mrow> </mrow> <mo>? </mo> </mover> </math> changes with time. <math> <mo>∴</mo> <mrow> <mi mathvariant="normal"> </mi> </mrow> </math> Statement (4) is incorrect.

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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 )