Question:
A particle of mass m is projected with a velocity v making an angle of 45$^{\circ}$ with the horizontal. The magnitude of the angular momentum of the projectile about the point of projection when the particle is at its maximum height h is
A particle of mass m is projected with a velocity v making an angle of 45$^{\circ}$ with the horizontal. The magnitude of the angular momentum of the projectile about the point of projection when the particle is at its maximum height h is
Updated On: Jun 14, 2022
- zero
- $mv^3 (4 \sqrt 2 g )$
- $ mv^3 (\sqrt 2 g ) $
- $ m \sqrt {2 g h^3} $
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The Correct Option is B
Solution and Explanation
$ L = m \frac{v }{\sqrt 2 } r_1$
Here,$ r_1 = h = \frac{v^2 sin ^2 45 ^ \circ }{ 2g} = \frac{ v^2}{4g} $
$ \therefore \, \, \, \, \, \, \, \, L = m \bigg( \frac{v}{ \sqrt 2} \bigg) \bigg( \frac{v^2}{4g} \bigg) = \frac{ mv^3}{ 4 \sqrt {2g}}$
Here,$ r_1 = h = \frac{v^2 sin ^2 45 ^ \circ }{ 2g} = \frac{ v^2}{4g} $
$ \therefore \, \, \, \, \, \, \, \, L = m \bigg( \frac{v}{ \sqrt 2} \bigg) \bigg( \frac{v^2}{4g} \bigg) = \frac{ mv^3}{ 4 \sqrt {2g}}$
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Concepts Used:
System of Particles and Rotational Motion
- The system of particles refers to the extended body which is considered a rigid body most of the time for simple or easy understanding. A rigid body is a body with a perfectly definite and unchangeable shape.
- The distance between the pair of particles in such a body does not replace or alter. Rotational motion can be described as the motion of a rigid body originates in such a manner that all of its particles move in a circle about an axis with a common angular velocity.
- The few common examples of rotational motion are the motion of the blade of a windmill and periodic motion.