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

Correct answer: A. 0.31 Density (ρ) = (mass)/(volume) (∆ ρ)/(ρ) = (∆ m)/(m) + (∆ V)/(V) = (∆ m)/(m) + (3 ∆ a)/(a) (∵ V = a ^ 3 ) =(0.1)/(10) + 3 ((0.01)/(0.1)) = 0.01 + 3 (0.1) = 0.31

JEE Main 20199 AprilMorning Shift

Exam: JEE Main
Year: 2019
Date: 9 April
Shift: Morning Shift
Subject: Physics
Chapter: Mathematics in Physics

JEE Main 2019 · 9 April · Morning Shift · Physics · Mathematics in Physics

In the density measurement of a cube, the mass and edge length are...

In the density measurement of a cube, the mass and edge length are measured as

\left(10.00 \pm 0.10\right)kg

and

\left(0.10 \pm 0.01\right)m,

respectively. The error in the measurement of density is:

Options

A $0.31$
B $0.10$
C $0.07$
D $0.01$

Correct answer

A. $0.31$

Step-by-step solution

Density

\left(ρ\right) = \dfrac{mass}{volume}

\dfrac{∆ ρ}{ρ} = \dfrac{∆ m}{m} + \dfrac{∆ V}{V}

= \dfrac{∆ m}{m} + \dfrac{3 ∆ a}{a} \left(∵ V = {a}^{3}\right) <br/>=\dfrac{0.1}{10} +

3 \left(\dfrac{0.01}{0.1}\right)

<br/>

= 0.01 + 3 \left(0.1\right)
= 0.31

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