First slide

Torque

Question

A force $\vec{F} = α \hat{i} + 3 \hat{j} + 6 \hat{k}$ is acting at a point $\vec{r} = 2 \hat{i} - 6 \hat{j} - 12 \hat{k}$ . The value of $α$ for which angular momentum about origin is conserved is

Moderate

A

1
B

-1
C

2
D

zero

Solution

Angular momentum will be conserved if net torque acting on the system about the origin becomes zero.
Given force acting $\vec{F} = α \hat{i} + 3 \hat{j} + 6 \hat{k}$ -----(i)
and $\vec{r} = 2 \hat{i} - 6 \hat{j} - 12 \hat{k} = - 2 (- \hat{i} + 3 \hat{j} + 6 \hat{k}) - - - - (ii)$
If torque becomes zero then then cross product should become zero. that is the two vectors must be parallel
$T h e r e f o r e, \frac{α}{2} = \frac{3}{- 6} = \frac{6}{- 12} \Rightarrow α = - 1$

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