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JEE Mains · Physics · STD 11 - System of particles and rotational motion
- JEE Mains 2013
- Medium
- MCQ
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
Pick an option to check your answer.
Answer & Solution
Correct Answer
(A) \( - 80\hat k\)
Step-by-step Solution
Detailed explanation
Angular momentum \(L = m\) \((v \times r)\)
\(\begin{array}{l}
= 2kg\,\left( {\frac{{dr}}{{dt}} \times r} \right) = 2\,kg\left( {4t\,j \times 5i - 2{t^2}\hat j} \right)\\
= 2\,kg\,\left( { - 20\,t\,\hat k} \right) = 2\,kg \times - 20 \times 2\,{m^{ - 2}}{s^{ - 1}}\hat k\\
= - 80\,\hat k
\end{array}\)
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