Question

The position of a particles varies with time as $\overrightarrow{r}=\alpha t^2\hat{i}-\beta t\hat{j}$ where $\alpha =10m{s}^{-2}$ and $\beta =5m{s}^{-1}$. The torque acting on the particle at t = 1s in N m is: (mass of the particle m = 0.1 kg)

• A. $5\hat{k}$
• B. $-3\hat{k}$
• C. $10\hat{k}$
• D. $-10\hat{k}$

Answer 1

The correct option is C $10\hat{k}$

$\overrightarrow{r}=10t^2\hat{i}-5t\hat{j}$
$\overrightarrow{V}=\frac{d\overrightarrow{r}}{dt}$
$=20t\hat{i}ˆ-5t\hat{j}$
$\overrightarrow{a}=20\hat{j}$
$\overrightarrow{F}=m\overrightarrow{a}$
$=\left(0.1\right)\left(20\right)\hat{i}$
$=2\hat{i}$
$\overrightarrow{r}=10\hat{i}-5\hat{j}$
$\overrightarrow{\tau }=\overrightarrow{r}\times \overrightarrow{F}$
$=(10\hat{i}-5\hat{j})\times 2\hat{i}$
$=10\hat{k}$