A body of mass 5 kg moving with a uniform speed in X - Y plane along the line . The angular momentum of the particle about the origin will be

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Solution

Q.
A body of mass 5 kg moving with a uniform speed $3 \sqrt{2} m s^{- 1}$ in X - Y plane along the line $y = x + 4$ . The angular momentum of the particle about the origin will be _____ $k g m^{2}$ $s^{- 1}$ . [2024]

Ans.
(60)    $y - x - 4 = 0$

$d_{1}$ is perpendicular distance of given line from origin.

   $d_{1} =$ $| \frac{- 4}{\sqrt{1^{2} + 1^{2}}} |$ $\Rightarrow 2 \sqrt{2} m$

So, $| \vec{L} |$ $= m v d_{1}$

   $= 5 \times 3 \sqrt{2} \times 2 \sqrt{2} kg m^{2} / s = 60 kg m^{2} / s$

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