JEE MAIN - Physics (2018 (Offline) - No. 23)
The density of a material in the shape of a cube is determined 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:
6%
2.5%
3.5%
4.5%
Explanation
Density of a material (d) = $${M \over {{L^3}}}$$
$$\therefore$$ Error in density,$${{\Delta d} \over d} = {{\Delta M} \over M} + 3{{\Delta L} \over L}$$
$${{\Delta d} \over d} \times 100 = {{\Delta M} \over M} \times 100 + 3{{\Delta L} \over L} \times 100$$
$$ \Rightarrow {{\Delta d} \over d} \times 100 = 1.5\% + 3\left( 1 \right)\% $$ = 4.5 %
$$\therefore$$ Error in density,$${{\Delta d} \over d} = {{\Delta M} \over M} + 3{{\Delta L} \over L}$$
$${{\Delta d} \over d} \times 100 = {{\Delta M} \over M} \times 100 + 3{{\Delta L} \over L} \times 100$$
$$ \Rightarrow {{\Delta d} \over d} \times 100 = 1.5\% + 3\left( 1 \right)\% $$ = 4.5 %
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