Mathematics in Physics

JEE Main level, single correct, medium

101 of 121

Question 101 of 121

In the density measurement of a cube, the mass and edge length are measured as (10.00±0.10)kg\left(10.00\pm 0.10\right)kg and (0.10±0.01)m,\left(0.10\pm 0.01\right)m, respectively. The error in the measurement of density is:

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Answer: (A) 0.310.31

Density (ρ)=massvolume\left(\rho \right)=\dfrac{mass}{volume}
∆ρρ=∆mm+∆VV\dfrac{∆\rho }{\rho }=\dfrac{∆m}{m}+\dfrac{∆V}{V}
=∆mm+3∆aa=\dfrac{∆m}{m}+\dfrac{3∆a}{a} (∵V=a3)\left(∵V={a}^{3}\right)
=0.110+3(0.010.1)=\dfrac{0.1}{10}+3\left(\dfrac{0.01}{0.1}\right)
=0.01+3(0.1)=0.01+3\left(0.1\right)
=0.31=0.31

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