A force of acts on the origin of the coordinate system. The torque about the point (2, - 3) is , the ratio of is . The value of is _____ . [2023]

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Solution

Q.
A force of $- P \hat{k}$ acts on the origin of the coordinate system. The torque about the point (2, - 3) is $P (a \hat{i} + b \hat{j})$ , the ratio of $\frac{a}{b}$ is $\frac{x}{2}$ . The value of $x$ is _____ . [2023]

Ans.
(3)

$τ = \vec{r} \times \vec{F}$

$Where \vec{r} = - 2 \hat{i} + 3 \hat{j}$

$τ = (- 2 \hat{i} + 3 \hat{j}) \times (- P \hat{k})$ $= P (- 2 \hat{j} - 3 \hat{i}) = P (- 3 \hat{i} - 2 \hat{j})$

$\Rightarrow So a = - 3, b = - 2$

$\frac{a}{b} = \frac{3}{2}$

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