Two identical masses are connected by a spring and placed on...

Two identical masses are connected by a spring and placed on a smooth surface. $\Lambda$ third identical mass moving with speed $y_{0}$ collides with one of the two masses elastically. Choose the correct option. (a) Centre of mass of the two blocks connected by spring moves with a constant speed after collision (b) 'Two blocks connected by spring oscillate about their centre of mass (c) Maximum compression in spring is $\sqrt{\frac{m v_{0}^{2}}{2 k}}$ (d) Maximum compression in spring is $\sqrt{\frac{m v_{i}^{2}}{k}}$

Two identical masses are connected by a spring and placed on a smooth surface. $\Lambda$ third identical mass moving with speed $y_{0}$ collides with one of the two masses elastically. Choose the correct option.
(a) Centre of mass of the two blocks connected by spring moves with a constant speed after collision
(b) 'Two blocks connected by spring oscillate about their centre of mass
(c) Maximum compression in spring is $\sqrt{\frac{m v_{0}^{2}}{2 k}}$
(d) Maximum compression in spring is $\sqrt{\frac{m v_{i}^{2}}{k}}$

Key Concepts

Elastic Collision

An elastic collision is one in which both kinetic energy and momentum are conserved. This principle is essential for analyzing interactions between bodies where no energy is lost to sound, heat, or deformation, allowing one to determine the post-collision velocities of the bodies involved.

Conservation of Momentum

The conservation of momentum principle states that in the absence of external forces, the total momentum of a system remains constant before and after any event such as a collision. This concept is crucial when studying systems of colliding bodies as it allows the prediction of their combined motion.

Center of Mass Motion

The center of mass of a system moves as though all external forces were acting on a single point with the total mass of the system. In isolated systems with only internal forces, such as those from springs connecting masses, the center of mass will continue moving at a constant velocity even as the masses oscillate about it.

Oscillatory Motion in Spring-Mass Systems

Masses connected by a spring can exhibit oscillatory motion when displaced from their equilibrium positions. This oscillation, typically described as simple harmonic motion, occurs about the system's center of mass, and its characteristics (such as period and amplitude) depend on factors like the spring constant and the mass values.

Maximum Spring Compression

The maximum compression in a spring during dynamic events is determined by the conversion of kinetic energy into elastic potential energy. By equating the kinetic energy lost by the moving masses to the energy stored in the spring, one can derive an expression for the maximum compression, a key aspect in analyzing the force and energy distribution in spring systems.

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