Solution to JEE Mains 2018 Physics Q1

Q1. 1. The density of a material in the shape of a cube is determines 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 :
(1) 2.5%
(2) 3.5%
(3) 4.5%
(4) 6%

Ans-

\[ Density(ρ)=\frac{Mass(M)}{Volume(V)}\]
Here, the material is cube (dimension, L).
\[ ρ=\frac{M}{L^{3}}\] \[ ρ={M}{L^{-3}}\]
Maximum error in determining the density
\[ \frac{\Delta \rho }{\rho}=\frac{\Delta M }{M}+\frac{3\Delta L }{L} \]
\[ \frac{\Delta \rho }{\rho}= 1.5 + 3 × 1 \]
=4.5%
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Combination of Errors:
1) Error of a sum or difference >
D = A + B, then maximum error in D will be ΔD = ΔA + ΔB
2) Error of a product or quotient >
a) D = AB, then the relative error in D is:
(ΔD/D) = (ΔA/A) + (ΔB/B)
b) \[D = {A^{3}}{B^{2}}{C^{-3}}\]
The relative error in D is
(ΔD/D) = 3(ΔA/A) + 2(ΔB/B) + 3 (ΔC/C) (Note: errors are always additive in nature (physics))
Why-errors-are-always-additive-in-nature-physics
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Type in latex