Mathematics in Physics

JEE Main level, numerical answer, medium

83 of 121

Question 83 of 121

For z=a2x3y12z={a}^{2}{x}^{3}{y}^{\dfrac{1}{2}}, where 'aa' is a constant. If percentage error in measurement of 'xx' and 'yy' are 44%and 1212%, respectively, then the percentage error for 'zz' will be _____%.

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Answer: 18

Given: z=a2x3y12z={a}^{2}{x}^{3}{y}^{\dfrac{1}{2}}
Relative error is given by
∆zz=[3×∆xx+12×∆yy]\dfrac{∆z}{z}=\left[3\times \dfrac{∆x}{x}+\dfrac{1}{2}\times \dfrac{∆y}{y}\right]
Now, maximum percentage error in zz is
∆zz×100=[3(4)+12(2)]×100\dfrac{∆z}{z}\times 100=\left[3\left(4\right)+\dfrac{1}{2}\left(2\right)\right]\times 100
=18=18%.

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