JEE Main On 08 April 2018 Question 25
Question: The density of a material in the shape of a cube is determined by measuring three sides of the cube and its mass. If the relative errors in measuring the mass and length are respectively 1.5% and 1%, the maximum error in determining the density is: [JEE Main Online 08-04-2018]
Options:
A) $ 4.5% $
B) $ 6% $
C) $ 2.5% $
D) $ 3.5% $
Show Answer
Answer:
Correct Answer: A
Solution:
$ \rho =\frac{m}{{{\ell }^{3}}} $
$ \frac{d\rho }{\rho }=\frac{dm}{m}+3\frac{d\ell }{\ell } $
$ \frac{d\rho }{\rho }\times 100=\frac{dm}{m}\times 100+3\frac{d\ell }{\ell }\times 100 $
$ =1.5+3\times 1=4.5% $
