A sphere of mass m moving the velocity v enters a hanging bag of sand and stops. If the mass of

step 1 A sphere of mass M moving with the velocity V enters a hanging bag of sands and stops. If the ma

A sphere of mass m moving the velocity v enters a hanging...

A sphere of mass $\mathrm{m}$ moving the velocity $\mathrm{v}$ enters a hanging bag of sand and stops. If the mass of the bag is $\mathrm{M}$ and it is raised by height $\mathrm{h}$, then the velocity of the sphere was (A) $[\{\mathrm{m}+\mathrm{M}\} / \mathrm{m}] \sqrt{(2 \mathrm{gh})}$ (B) $(\mathrm{M} / \mathrm{m}) \sqrt{(} 2 \mathrm{gh})$ (C) $[\mathrm{m} /\{\mathrm{M}+\mathrm{m}\}] \sqrt{(2 \mathrm{gh})}$ (D) $(\mathrm{m} / \mathrm{M}) \sqrt{(2 \mathrm{gh})}$

A sphere of mass $\mathrm{m}$ moving the velocity $\mathrm{v}$ enters a hanging bag of sand and stops. If the mass of the bag is $\mathrm{M}$ and it is raised by height $\mathrm{h}$, then the velocity of the sphere was
(A) $[\{\mathrm{m}+\mathrm{M}\} / \mathrm{m}] \sqrt{(2 \mathrm{gh})}$
(B) $(\mathrm{M} / \mathrm{m}) \sqrt{(} 2 \mathrm{gh})$
(C) $[\mathrm{m} /\{\mathrm{M}+\mathrm{m}\}] \sqrt{(2 \mathrm{gh})}$
(D) $(\mathrm{m} / \mathrm{M}) \sqrt{(2 \mathrm{gh})}$

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Key Concepts

Inelastic Collision

An inelastic collision is one in which the colliding bodies stick together or otherwise lose kinetic energy in the process of colliding. Although kinetic energy is not conserved, momentum is, and the loss of kinetic energy is typically transformed into other forms of energy, such as potential energy or heat.

Conservation of Momentum

This principle states that the total momentum of a closed system remains constant if no external forces act on it. In collision problems, even if the kinetic energy is not conserved (as in an inelastic collision), the momentum before and after the collision must balance, which is crucial for determining the system’s velocity immediately after impact.

Energy Transformation

Energy transformation involves the conversion of one type of energy into another. In dynamics problems, kinetic energy can be converted into gravitational potential energy, such as when a moving mass comes to rest by rising against gravity. This conversion allows the use of energy conservation ideas to relate the initial kinetic energy to the height gained by the mass.

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