# A physical quantity p depends on the other two physical quantities Q and R, as follows P = $a Q ^2 R^{ 1/2}$ Where a is constant. In an experiment, the quantity Q is determined by measuring P and R and using The above expression. If the percentage of error in measurement of P and R is 10 % and 12 % respectively, Then the % age of error in determines the value of Q is

Given P = $a Q ^2 R^{ 1/2}$

$Q=\frac{P^\frac{1}{2}}{aR^\frac{1}{4}}$

$\frac{\Delta Q}{Q} *100= \frac{\Delta P }{2P} *100+ \frac{1}{4} \frac{\Delta R}{R} *100error \: \: in \: \: Q \Rightarrow \frac{\Delta Q}{Q} *100=\frac{10}{2}+\frac{12}{4}=8$

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