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

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Q.
A particle of mass m projected with a velocity 'u' making an angle of 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 h is _____. [2024]

1 $\frac{\sqrt{3}}{16} \frac{m u^{3}}{g}$

2 $\frac{\sqrt{3}}{2} \frac{m u^{2}}{g}$

3 $\frac{m u^{3}}{\sqrt{2} g}$

4 zero

Ans.
(1)

Velocity of particle at maximum height

$v = u \cos 30 ° = \frac{u \sqrt{3}}{2}$

Maximum height, $h = \frac{u^{2} \sin^{2} 30 °}{2 g} = \frac{u^{2}}{8 g}$

Magnitude of angular momentum

$| \vec{L} |$ $= h m v$

$= (\frac{u^{2}}{8 g}) m (\frac{u \sqrt{3}}{2}) = \frac{\sqrt{3} m u^{3}}{16 g}$

Solution

Q.
A particle of mass m projected with a velocity 'u' making an angle of 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 h is _____. [2024]

1 $\frac{\sqrt{3}}{16} \frac{m u^{3}}{g}$

2 $\frac{\sqrt{3}}{2} \frac{m u^{2}}{g}$

3 $\frac{m u^{3}}{\sqrt{2} g}$

4 zero

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Solution

Q. A particle of mass m projected with a velocity 'u' making an angle of 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 h is _____. [2024]

1 3 16 mu3g

2 3 2 mu2g

3 mu32g

4 zero

Ans. (1) Velocity of particle at maximum height v=ucos30°=u32 Maximum height, h=u2sin230°2g=u28g Magnitude of angular momentum |L→|=hmv =(u28g)m(u32)=3mu316g

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Q.
A particle of mass m projected with a velocity 'u' making an angle of 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 h is _____. [2024]

1 $\frac{\sqrt{3}}{16} \frac{m u^{3}}{g}$

2 $\frac{\sqrt{3}}{2} \frac{m u^{2}}{g}$

3 $\frac{m u^{3}}{\sqrt{2} g}$