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JEE Main 202430 JanuaryMorning Shift
Exam
JEE Main
Year
2024
Date
30 January
Shift
Morning Shift
Subject
Physics
Chapter
Motion in Two Dimensions

JEE Main 2024 · 30 January · Morning Shift · Physics · Motion in Two Dimensions

A particle of mass m projected with a velocity u making an angle of...

A particle of mass mm projected with a velocity uu making an angle of 30°30 ° with the horizontal. The magnitude of angular momentum of the projectile about the point of projection when the particle is at its maximum height hh is :

Options

  1. A316mu3g\dfrac{\sqrt{3}}{16}\dfrac{m{u}^{3}}{g}
  2. B32mu2g\dfrac{\sqrt{3}}{2}\dfrac{m{u}^{2}}{g}
  3. Cmu32g\dfrac{m{u}^{3}}{\sqrt{2}g}
  4. Dzero

Correct answer

A. 316mu3g\dfrac{\sqrt{3}}{16}\dfrac{m{u}^{3}}{g}

Step-by-step solution

Angular momentum at maximum height will be, L=(mucosθ)hL = \left(mucos\theta\right)h, where h=h =maximum height

Therefore, L=mucosθ×u2sin⁡2θ2gL = mucos\theta \times \dfrac{{u}^{2}\sin^{2}\theta}{2g}

=mu32g×32×(12)2=3mu316g= \dfrac{m{u}^{3}}{2g} \times \dfrac{\sqrt{3}}{2} \times {\left(\dfrac{1}{2}\right)}^{2} = \dfrac{\sqrt{3}m{u}^{3}}{16g}

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