Two identical beads of m=100 g are connected by an inextensible massless string that can slide

step 1 In this question we have given two identical beads of mass 100 gram and both are connected by an

Two identical beads of m=100 g are connected by an...

Two identical beads of $m=100 \mathrm{~g}$ are connected by an inextensible massless string that can slide along the two arms $A C$ and $B C$ of a rigid smooth wireframe in a vertical plane. If the system is released from rest, the kinetic energy of the first particle when they have moved by a distance of $0.1 \mathrm{~m}$ is $16 x \times 10^{-3} \mathrm{~J}$. Find the value of $x .\left(g=10 \mathrm{~m} / \mathrm{s}^{2}\right)$

Two identical beads of $m=100 \mathrm{~g}$ are connected by an inextensible massless string that can slide along the
two arms $A C$ and $B C$ of a rigid smooth wireframe in a vertical plane. If the system is released from rest, the kinetic energy of the first particle when they have moved by a distance of $0.1 \mathrm{~m}$ is $16 x \times 10^{-3} \mathrm{~J}$. Find the value of $x .\left(g=10 \mathrm{~m} / \mathrm{s}^{2}\right)$

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Key Concepts

Gravitational Potential Energy

Gravitational potential energy represents the energy an object possesses due to its position in a gravitational field. As the object moves vertically within the field, changes in its potential energy are converted into kinetic energy, facilitating the analysis of energy transformations in the system.

Kinetic Energy in Constrained Motion

Kinetic energy quantifies the energy of motion of an object. In systems where motion is constrained by factors such as fixed string lengths or smooth surfaces, understanding how these constraints influence the speed and direction of the moving parts is essential for correctly calculating the kinetic energy.

Conservation of Energy

This principle states that the total mechanical energy (the sum of potential and kinetic energy) in an isolated system remains constant if no non-conservative forces (like friction) work on the system. It is used to relate the decrease in gravitational potential energy to the increase in kinetic energy as a system evolves.

Inextensible String Constraint

An inextensible string is one that does not change its length, meaning that the motion of any objects attached to it is linked. This constraint creates a relationship between the displacements, velocities, and accelerations of the connected masses, which is vital for analyzing the system's dynamics.

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