Verified Solution • 2025–26 Session moderate

QJEEM24Phd689: JEE Main 2024 Physics - Class 11 JEEM24Phd689 Solution: A particle of mass is projected with a velocity ' ' making an…

A particle of mass m\mathrm{m} is projected with a velocity ' u\mathrm{u} ' making an angle of 30∘30^{\circ} with the horizontal. The magnitude of angular momentum of the projectile about the point of projection when the particle is at its maximum height h\mathrm{h} is :

Multiple Choice Options

  • A mu32 g\frac{\mathrm{mu}^3}{\sqrt{2} \mathrm{~g}}
  • B zero
  • C 32mu2 g\frac{\sqrt{3}}{2} \frac{\mathrm{mu}^2}{\mathrm{~g}}
  • D 316mu3 g\frac{\sqrt{3}}{16} \frac{\mathrm{mu}^3}{\mathrm{~g}}

Step-by-Step Verified Solution

amp;L=mucos⁡θHamp;=mucos⁡θ×u2sin⁡2θ2gamp;=mu32g×32×(12)2=3mu316g\begin{aligned}& \mathrm{L}=m u \cos \theta H \\& =m u \cos \theta \times \frac{u^2 \sin ^2 \theta}{2 g} \\& =\frac{m u^3}{2 g} \times \frac{\sqrt{3}}{2} \times\left(\frac{1}{2}\right)^2=\frac{\sqrt{3} m u^3}{16 g}\end{aligned}

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