JEE Main · 2024 · 30 Jan 2024 · Shift 1 · Kinematics

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

3 0^{\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

is :

(A) $\frac{3}{16} \frac{m u ^{3}}{g}$ ✓ Correct
(B) $\frac{3}{2} \frac{m u ^{2}}{g}$
(C) $\frac{m u ^{3}}{2 g}$
(D)zero

Answer: (A)

Solution

At maximum height only the horizontal component

u cos 3 0^{\circ}

survives, and

h = \frac{u ^{2} sin ^{2} 3 0 ^{\circ}}{2 g}

L = m (u cos 3 0^{\circ}) h = m u \cdot \frac{3}{2} \cdot \frac{u ^{2} ( 1/4 )}{2 g} = \frac{3}{16} \frac{m u ^{3}}{g}

JEE Main · 2024 · 30 Jan 2024 · Shift 1 · Single correct option

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