Published by:
CGP EDU Academic Team
Published on: September 12, 2026
Two beads each of mass m are fixed on a light rigid rod of length 
which is free to rotate in a horizontal plane. The bead on the far end is given some velocity v as shown in the figure. If K cm represents the kinetic energy of the centre of mass of the system and K R represents the rotational kinetic energy of the system, then what is the value of 
?
Text Solution
Verified by ExpertsThe correct answer is:
A
Step 1: Calculate the kinetic energy of the center of mass (K cm) of the system. The center of mass can be calculated by taking into account the mass and velocities of both beads.
Step 2: Calculate the rotational kinetic energy (K R) of the system using the formula \( K_R = \frac{1}{2} I \omega^2 \), where I is the moment of inertia of the system.
Step 3: The relation between K cm and K R can be determined. The sum of translational kinetic energy and rotational kinetic energy should equal the total energy.
By analyzing the dynamics of the rotating system, the value of \( \frac{K_{cm}}{K_{R}} \) can be deduced and is found to be 2, thus the final answer is \( 2 \). Therefore, A.
Step 2: Calculate the rotational kinetic energy (K R) of the system using the formula \( K_R = \frac{1}{2} I \omega^2 \), where I is the moment of inertia of the system.
Step 3: The relation between K cm and K R can be determined. The sum of translational kinetic energy and rotational kinetic energy should equal the total energy.
By analyzing the dynamics of the rotating system, the value of \( \frac{K_{cm}}{K_{R}} \) can be deduced and is found to be 2, thus the final answer is \( 2 \). Therefore, A.
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