Physics - Rotation Question with Solution | TestHub

The torque $\vec{\tau }$ acting on an object is given by the cross product of the position vector $\vec{r}$ and the force vector $\vec{F}$.

$\vec{\tau }=\vec{r}\times \vec{F}$

Given $\vec{r}=4\hat{i}-3\hat{j}$ and $\vec{F}=5\hat{i}-10\hat{j}$, we can calculate the cross product using the determinant method:

$\vec{\tau }=\left|\begin{array}{ccc}\hat{i}& \hat{j}& \hat{k}\\ 4& -3& 0\\ 5& -10& 0\end{array}\right|$

Expanding the determinant along the first row:

$\vec{\tau }=\hat{i}(0-0)-\hat{j}(0-0)+\hat{k}[4(-10)-(-3)(5)]$

$\vec{\tau }=\hat{k}[-40+15]$

$\vec{\tau }=-25\hat{k}$

Answer: $-25\hat{\mathrm{k}}$