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6.System of Particles and Rotational Motion
medium
A particle of mass $2\, kg$ is moving such that at time $t$, its position, in meter, is given by $\overrightarrow r \left( t \right) = 5\hat i - 2{t^2}\hat j$ . The angular momentum of the particle at $t\, = 2\, s$ about the origin in $kg\, m^{-2}\, s^{-1}$ is
A
$ - 80\hat k$
B
$\left( {10\hat i - 16\hat j} \right)$
C
$ - 40\hat k$
D
$ 40\hat k$
(JEE MAIN-2013)
Solution
Angular momentum $L = m$ $(v \times r)$
$\begin{array}{l}
= 2kg\,\left( {\frac{{dr}}{{dt}} \times r} \right) = 2\,kg\left( {4t\,j \times 5i – 2{t^2}\hat j} \right)\\
= 2\,kg\,\left( { – 20\,t\,\hat k} \right) = 2\,kg \times – 20 \times 2\,{m^{ – 2}}{s^{ – 1}}\hat k\\
= – 80\,\hat k
\end{array}$
Standard 11
Physics
