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$\mathrm{O}(0,0), \mathrm{A}(0,3), \mathrm{B}(4,0)$ are the vertices of triangle $\mathrm{OAB}$.
A force $10 \hat{\mathrm{i}}$ acts at $\mathrm{B}$. What is the magnitude of moment of force about the vertex $\mathrm{A}$ ?
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A force $10 \hat{\mathrm{i}}$ acts at $\mathrm{B}$. What is the magnitude of moment of force about the vertex $\mathrm{A}$ ?
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Verified Answer
The correct answer is:
30 unit
As given:
$\mathrm{O}(0,0), \mathrm{A}(0,3), \mathrm{B}(4,0)$ are the vertices of triangle
OAB
$\therefore \overrightarrow{\mathrm{OA}}=\overrightarrow{\mathrm{r}}=3 \hat{\mathrm{j}}$ and $\overrightarrow{\mathrm{F}}=10 \hat{\mathrm{i}}$
Movement of force about the vertex
$\mathrm{A}=\overrightarrow{\mathrm{r}} \times \overrightarrow{\mathrm{F}}=3 \hat{\mathrm{j}} \times 10 \hat{\mathrm{i}}=-30 \hat{\mathrm{k}}$
$\therefore \quad$ Magnitude of moment $=|30 \hat{\mathrm{k}}|=30$ unit
$\mathrm{O}(0,0), \mathrm{A}(0,3), \mathrm{B}(4,0)$ are the vertices of triangle
OAB
$\therefore \overrightarrow{\mathrm{OA}}=\overrightarrow{\mathrm{r}}=3 \hat{\mathrm{j}}$ and $\overrightarrow{\mathrm{F}}=10 \hat{\mathrm{i}}$
Movement of force about the vertex
$\mathrm{A}=\overrightarrow{\mathrm{r}} \times \overrightarrow{\mathrm{F}}=3 \hat{\mathrm{j}} \times 10 \hat{\mathrm{i}}=-30 \hat{\mathrm{k}}$
$\therefore \quad$ Magnitude of moment $=|30 \hat{\mathrm{k}}|=30$ unit
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