- #1
Robin04
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Homework Statement
The density of a rod in function of space is given as ##\rho (x)=\frac{c}{x^2}##
1. What kind of density is this?
2. What is the dimension of ##c##?
3. What is the mass of the rod in the intervals
- [1 m, 2 m],
- (1 m, 2 m),
- (0 m, 1 m),
- [0 m, 1 m]?
4. Can a plate with such density exist?
Homework Equations
The Attempt at a Solution
1. Assuming this is a thin rod with infinitesimal cross section area, this should be a linear density function.
2. Therefore ##[c]=kg \cdot m##
3. For the interval [1m,2m] it is obvious that ##m_1 = \int_{1}^{2}\rho (x) dx = \frac{c}{2}##
But how do I evaluate the integral on an open interval? Also, the intervals having 0 as their beginning (either open or closed) should imply an infinite mass, right?