JEE Mains · Physics · STD 11 - Units,dimensions and measurement
- JEE Mains 2019
- Hard
- MCQ
In the density measurement of a cube, the mass and edge length are measured as \((10.00 \pm 0.10)\,\,kg\,\) and \((0.10 \pm 0.01)\,\,m\,\) respectively. The error in the measurement of density is
Pick an option to check your answer.
Answer & Solution
Correct Answer
(D) None of these
Step-by-step Solution
Detailed explanation
\(\begin{array}{l} \rho = \frac{m}{v}\\ Maximum\,\% \,error\,in\,\rho \,will\,be\,given\,by\\ \frac{{\Delta p}}{p} \times 100\% = \left( {\frac{{\Delta m}}{m}} \right) \times 100\% + 3\left( {\frac{{\Delta L}}{L}} \right) \times 100\% \,\,...\left( i \right)\\ This\,is\,not\,applicable\,as\,error\,is\,big. \end{array}\)
\(\begin{array}{l} {\rho _{\min }} = \frac{{{m_{\min }}}}{{{v_{\max }}}} = \frac{{9.9}}{{{{\left( {0.11} \right)}^3}}} = 7438kg/{m^3}\\ and \,{\rho _{\max \,}} = \frac{{{m_{\max }}}}{{{v_{\min }}}} = \frac{{10.1}}{{{{\left( {0.09} \right)}^3}}} = 13854.6kg/{m^3}\\ \Delta \rho = 6416.6\,\,kg/{m^3}\\ \end{array}\)
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