Question

The solid cylinder D with density rho=5e −r 2 has ______.

A) Uniform Density
B) Increasing Density
C) Decreasing Density
D) Radial Density Gradient

Answer 1

The solid cylinder D with density rho=5e^-r^2 has a C. Decreasing Density with the increasing radius.

Step-by-step explanation:

The solid cylinder D with density ρ=5e⁻¹² exhibits a Decreasing Density as the distance r from the central axis increases, because the density function is an exponential decay function of r. In real-world terms, an object that has a density decreasing with the radius, like the given cylinder, would be less dense the farther away you get from the center. This concept is integral to understanding how various charge densities affect the electric and gravitational fields around an object.

The solid cylinder D with density ρ=5e −r 2 has a decreasing density. The expression ρ=5e −r 2 tells us that the density of the cylinder decreases as the radius (r) increases. This means that as you move from the center of the cylinder towards the outer surface, the density decreases.