The relative density of a material of a body is found by weighing it first in air and then in water. If the weight of the body in air is $W_{1} = 8.00 \pm 0.05 N$ and the weight in water is $W_{2} = 6.00 \pm 0.05 N$ , then the relative density $ρ_{r} = W_{1} / (W_{1} - W_{2})$ with the maximum permissible error is

see full answer

Talk to JEE/NEET 2025 Toppers - Learn What Actually Works!

Real Strategies. Real People. Real Success Stories - Just 1 call away

An Intiative by Sri Chaitanya

$4.00 \pm 5.62 %$

$4.00 \pm 0.62 %$

$4.00 \pm 3.2 %$

$4.00 \pm 0.82 %$

answer is D.

(Unlock A.I Detailed Solution for FREE)

Ready to Test Your Skills?

Check your Performance Today with our Free Mock Test used by Toppers!

Take Free Test

Detailed Solution

$\begin{array}{l} Relative density ρ_{r} = \frac{W_{1}}{W_{1} - W_{2}} = \frac{8.00}{8.00 - 6.00} = 4.00 \\ \begin{aligned} \frac{Δ ρ_{r}}{ρ_{r}} \times 100 & = \frac{Δ W_{1}}{W_{1}} \times 100 + \frac{Δ (W_{1} - W_{2})}{W_{1} - W_{2}} \times 100 \\ = \frac{0.05}{8.00} \times 100 + \frac{0.05 + 0.05}{2} \times 100 = 5.62 % \end{aligned} \\ ∴ ρ_{r} = 4.00 \pm 5.62 % \end{array}$