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QJEEM24Ph0890: JEE Main 2024 Physics - Class 11 JEEM24Ph0890 Solution: A body of mass moving with a uniform speed in plane along the…

A body of mass 5 kg5 \mathrm{~kg} moving with a uniform speed 32 ms−13 \sqrt{2} \mathrm{~ms}^{-1} in X−YX-Y plane along the line y=x+4y=x+4 . The angular momentum of the particle about the origin will be _________ kg m2 s−1\mathrm{kg} \mathrm{~m}^2 \mathrm{~s}^{-1} .

Step-by-Step Verified Solution

y−x−4=0y-x-4=0

d1d_1 is perpendicular distance of given line from origin.

d1=∣−412+12∣⇒22 m\mathrm{d}_1=\left|\frac{-4}{\sqrt{1^2+1^2}}\right| \Rightarrow 2 \sqrt{2} \mathrm{~m}

So

∣L→∣=mvd1amp;=5×32×22 kg m2/samp;=60 kg m2/s\begin{aligned}|\overrightarrow{\mathrm{L}}|=\mathrm{mvd}_1 & =5 \times 3 \sqrt{2} \times 2 \sqrt{2} \mathrm{~kg} \mathrm{~m}^2 / \mathrm{s} \\& =60 \mathrm{~kg} \mathrm{~m}^2 / \mathrm{s}\end{aligned}

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