At time t = 0 , a 2 , kg particle has position vector r = ( 4 i -… - Vidyadip

MCQ

At time $t = 0$ , a $2\, kg$ particle has position vector $\vec r = \left( {4\hat i - 2\hat j} \right)\,m$ relative to the origin. Its velocity is given by $\vec v = 2{t^2}\hat i\,\left( {m/s} \right)$. The torque acting on the particle about the origin at $t = 2\,s$, is ........ $\hat k\,N - m$

✓
$32$
B
$-16$
C
$16$
D
$122$

✓

Answer

Correct option: A.

$32$

a
$\vec{\tau}=\frac{\mathrm{d} \overrightarrow{\mathrm{J}}}{\mathrm{dt}}=\frac{\mathrm{d}}{\mathrm{dt}}(\overrightarrow{\mathrm{r}} \times \mathrm{p})=\mathrm{m} \frac{\mathrm{d}}{\mathrm{dt}}(\overrightarrow{\mathrm{r}} \times \overrightarrow{\mathrm{v}})$

$\vec{\tau}=[16 \mathrm{t}] \hat{\mathrm{k}}$

at $\mathrm{t}=2 \quad \vec{\tau}_{\mathrm{t}=2}=(16 \times 2) \hat{\mathrm{k}}=32 \hat{\mathrm{k}} \quad \mathrm{N}-\mathrm{m}$

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