A force \mathop \text{F}\limits^ \to = \alpha \hat i + 3\hat j + 6\hat k is acting at a point \mathop \text{r}\limits^ \to = 2\hat i - 6\hat j - 12\hat k. The value of α for which angular momentum about origin is conserved is:

 

  • Option 1)

    2

  • Option 2)

    zero

  • Option 3)

    1

  • Option 4)

    -1

 

Answers (1)
V Vakul

 

Torque -

underset{	au }{
ightarrow}= underset{r}{
ightarrow}	imes underset{F}{
ightarrow}   

 

- wherein

This can be calculated by using either  	au=r_{1}F; or; 	au=rcdot F_{1}

r_{1} = perpendicular distance from origin to the line of force.

F_{1} = component of force perpendicular to line joining force.

 

 

 L= r^{\rightarrow }\times p^{\rightarrow } = \ constant

\begin{vmatrix} 2, -6, -12 \end {vmatrix}            


Option 1)

2

This option is incorrect.

Option 2)

zero

This option is incorrect.

Option 3)

1

This option is correct.

Option 4)

-1

This option is incorrect.

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