Question about calculating age of a uranium and lead containing object, based on the ratio of uranium-to-lead I realize this is probably going to sound so stupid, but... here goes:
Radioactive decay: We know that we can calculate the age of a uranium containing object by the uranium-to-lead ratio, due to uranium’s constant rate of deterioration into lead.  But, what if the object (e.g., a rock) was once part of a larger object that broke off?  Wouldn’t the uranium-to-lead ratio in the smaller object be misleading, having once been a part of a greater whole with its own uranium-to-lead ratio? (i.e., Wouldn’t the smaller, “break-off-piece” of rock just contain a fraction of the larger piece’s total quantity of uranium and lead—which until the point of separation was a part of the entire quantity of uranium and lead of the larger rock, and could have been used in conjunction with the rest of the larger rock’s uranium-to-lead ratio to determine the larger rock’s age—which would make the smaller rock appear younger/older than it really is?) Moreover, wouldn’t the age of the larger object then be misleading, because a smaller (uranium and lead containing) piece of it has broken off, altering the ratio of uranium-to-lead, and thus skewing the total amount of each element used in calculating the ratio which tells us its age?
 A: When these techniques are used, there is an assumption that the distribution of minerals/elements is uniform throughout the object. The whole point of using a ratio technique is that the size of the sample becomes unimportant.
It's like a food company making pancake mix: they don't mix each box individually.  If they have mix 20 lbs of flour to 1 lb of sugar, every box is still going to have a 20:1 ratio of flour to sugar.
Breaking the rock into smaller pieces is assumed to not change the ratio (what argument can you make that it should?) and it definitely doesn't change the decay rates.
A: Well your apprehensions are there but the geologists working  on this method have taken precautions for comparing their results through  a variety of  radioactive decay series and using zircon in crystal forms
The followung details may be seen in the citations listed (from Wikipedia):

Undamaged zircon retains the lead generated by radioactive decay of uranium and thorium until very high temperatures (about 900 °C), though accumulated radiation damage within zones of very high uranium can lower this temperature substantially.
Zircon is very chemically inert and resistant to mechanical weathering—a mixed blessing for geochronologists, as zones or even whole crystals can survive melting of their parent rock with their original uranium-lead age intact.
Zircon crystals with prolonged and complex histories can thus contain zones of dramatically different ages (usually, with the oldest and youngest zones forming the core and rim, respectively, of the crystal), and thus are said to demonstrate inherited characteristics.
Unraveling such complications (which, depending on their maximum lead-retention temperature, can also exist within other minerals) generally requires in situ micro-beam analysis via, say, ion microprobe (SIMS) or laser ICP-MS.>

References:

*

*https://en.wikipedia.org/wiki/Uranium-lead_dating


*Mattinson, J.M., 2005. Zircon U-Pb Chemical abrasion (“CA-TIMS”) method: Combined annealing and multi-step dissolution analysis for Improved precision and accuracy of zircon ages. Chemical Geology. 220, 47-66.


*Dickin, A.P., 2005. Radiogenic Isotope Geology 2nd ed. Cambridge: Cambridge University Press. pp. 101.
