Math Problem Statement

Four rigid bodies with identical masses M and radii r were made to roll without slipping from the same height on a quarter circle of radius R. All of them are moving horizontally as they leave the ramp. The spheres hit the ground at the same time t. If L is the range reached by the rigid bodies, which of the following is the correct arrangement of the rigid bodies in terms of increasing L? The options are: 1. III, I, IV, II 2. II, IV, I, III 3. IV, II, III, I 4. I, II, III, IV.

Solution

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Math Problem Analysis

Mathematical Concepts

Kinematics
Rotational Dynamics
Conservation of Energy

Formulas

Kinetic energy for rolling objects: K = (1/2)mv^2 + (1/2)Iω^2
Moment of inertia for solid and hollow spheres and cylinders
Range of projectile motion: L = v * t

Theorems

Conservation of Mechanical Energy
Moment of Inertia Calculations

Suitable Grade Level

Undergraduate Physics