Physics And Measurement Question 296
Question: The density of a sphere is measured by measuring its mass and diameter. If, it is known that the maximum percentage errors in the measurement are 2% and 3%, then find the maximum percentage error in the measurement of density?
Options:
A) 15%
B) 18%
C) 9%
D) 11%
Show Answer
Answer:
Correct Answer: D
Solution:
[d] Let m and d be the mass and diameter of the sphere, then the density p of the sphere is given by $ \rho =\frac{mass}{volume}=\frac{m}{\frac{4}{3}\pi {{( \frac{d}{2} )}^{3}}}=\frac{6m}{\pi d^{3}} $
$ or{{( \frac{d\rho }{\rho }\times 100 )} _{\max }}=| \frac{dm}{m}\times 100 |+| \frac{3d(d)}{d}\times 100 | $
$ =2+3(3)=11% $
