# Sphere moving at relativistic velocities

I stumbled upon this exercise on a SR book: Determine how fast a sphere of diameter 2R has to move to pass through a hole of diameter d on a planar surface.

If I understand correctly, this should not be possible because no mater how fast we are moving in one direction (a boost in the x direction w.l.o.g), the lengths of the sphere measured in the z and y axis will continue to be the same and won't suffer from length contraction. Am I missing something or the exercise is just that trivial? Thanks a lot for your help

• My reaction is the same as yours. I think it is "just that trivial" to someone who actually understands a little SR -- but understanding a little SR may not be so trivial! – user4552 Mar 20 '18 at 1:37
• I would reject any problem, on principle, that labels a diameter $R$. – JEB Mar 20 '18 at 1:40
• @JEB, to be fair, the diameter is labeled 2R, so the radius would be R as expected. – R. Elder Mar 20 '18 at 2:16
• Your understanding is spot on: a Lorentz boost transforms only the spatial co-ordinate along the direction of relative motion. Could you please add the text of the question and a citation? I'd like to know whether it is worded such that a "trick" trivial answer (i.e. it's not possible) is implied; otherwise it's a misleading question that could sabotage students' understanding - it would be a good catch on your part and would warrant a community Wiki answer to confirm. – Selene Routley Mar 20 '18 at 2:46
• Since you appear to be a fairly new user and might not be aware that @WetSavannaAnimalakaRodVance is pretty much always right, I'd like to confirm that he is certainly right in this case. – WillO Mar 20 '18 at 3:36