Question:
A particle of mass m is projected at velocity at a velocity u, making an angle θ with the horizontal(x-axis). If the angle of projection θ is varied keeping all other parameters same, then magnitude of angular momentum(L) at its maximum height about the point of projection varies with θ as,
A particle of mass m is projected at velocity at a velocity u, making an angle θ with the horizontal(x-axis). If the angle of projection θ is varied keeping all other parameters same, then magnitude of angular momentum(L) at its maximum height about the point of projection varies with θ as,
Updated On: Feb 15, 2025
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The Correct Option is D
Solution and Explanation
The magnitude of angular momentum (L) at its maximum height about the point of projection remains constant as the angle of projection (θ) is varied. The angular momentum is determined by the cross product of the particle's position vector and its linear momentum vector. Since both the position vector and linear momentum vector rotate in the same plane with respect to each other, their relative orientation does not change as the angle of projection changes. Consequently, the magnitude of angular momentum remains the same regardless of the value of θ.
The correct option is(D): 
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Concepts Used:
Rotational Motion
Rotational motion can be defined as the motion of an object around a circular path, in a fixed orbit.
Rotational Motion Examples:
The wheel or rotor of a motor, which appears in rotation motion problems, is a common example of the rotational motion of a rigid body.
Other examples:
- Moving by Bus
- Sailing of Boat
- Dog walking
- A person shaking the plant.
- A stone falls straight at the surface of the earth.
- Movement of a coin over a carrom board
Types of Motion involving Rotation:
- Rotation about a fixed axis (Pure rotation)
- Rotation about an axis of rotation (Combined translational and rotational motion)
- Rotation about an axis in the rotation (rotating axis)