A body of mass M is dropped from a height h on a sand floor....

A body of mass $M$ is dropped from a height $h$ on a sand floor. If the body penetrates $x \mathrm{~cm}$ into the sand, the average resistance offered by the sand to the body is (a) $M g\left(\frac{h}{x}\right)$ (b) $M g\left(1+\frac{h}{x}\right)$ (c) $M g h+M g x$ (d) $M g\left(1-\frac{h}{x}\right)$

A body of mass $M$ is dropped from a height $h$ on a sand floor. If the body penetrates $x \mathrm{~cm}$ into the sand, the average resistance offered by the sand to the body is
(a) $M g\left(\frac{h}{x}\right)$
(b) $M g\left(1+\frac{h}{x}\right)$
(c) $M g h+M g x$
(d) $M g\left(1-\frac{h}{x}\right)$

Key Concepts

Average Resistive Force Calculation

When an object moving with a certain kinetic energy encounters a resistive medium that brings it to rest over a known distance, the average resistive force can be determined by equating the work done by this force to the initial kinetic energy of the object. This concept allows for calculating the force based on energy considerations without detailing the force's variability during the interaction.

Gravitational Potential Energy

Gravitational potential energy refers to the energy stored in an object due to its position in a gravitational field. It is proportional to the object's mass, the gravitational acceleration, and its height above a reference level. This energy becomes available when the object is allowed to fall, serving as the initial energy reservoir for further conversion during impact.

Energy Conservation

This principle states that in a closed system, the total energy remains constant. When a body falls, its gravitational potential energy is converted into kinetic energy, and upon impact with a resistive medium, that kinetic energy is further transformed into work done against the resistance. This concept is fundamental in understanding energy transformations in dynamics.

Work-Energy Theorem

The work-energy theorem connects the work done by forces acting on an object to its change in kinetic energy. In cases involving resistive forces, such as a medium offering resistance during penetration, the work done by the resistive force is equal to the kinetic energy that the object loses. This theorem is instrumental in linking force and energy dissipation.

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