A12.0-cm long cylindrical rod has a uniform cross-sectional area a = 5.00 cm2. however, its density increases linearly from 2.60 g/cm3 at one end to 18.5 g/cm3 at the other end. this linearly increasing density can be described using the equation = b + cx. (a) find the constants b and c required for this rod, assuming the low-density end is placed at x = 0 cm and the high-density end is at x = 12 cm. (b) the mass of the rod can be found using: m=dv=adx=(b+cx)adx

(a) The constants required describing the rod's density are B=2.6 and C=1.325.

(b) The mass of the road can be found using

Explanation:

(a) Since the density variation is linear and the coordinate x begins at the low-density end of the rod, we have a density given by

recalling that the coordinate x is measured in centimeters.

(b) The mass of the rod can be found by having into account the density, which is x-dependent, and the volume differential for the rod:

,

hence, the mass of the rod is 126.6 g.

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