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NEET 2013

Exam: NEET
Year: 2013
Subject: Physics
Chapter: Mathematics in Physics

NEET 2013 · Physics · Mathematics in Physics

In an experiment four quantities a, b, c and d are measured with...

In an experiment four quantities

a, b, c

and

d

are measured with percentage error

1 \%, 2 \%, 3 \%

and

4 \%

respectively. Quantity

P

is calculated as follows

P=\frac{a^3 b^2}{c d} \%

, Error in

P

is

Options

A $14 \%$
B $10 \%$
C $7 \%$
D $4 \%$

Correct answer

A. $14 \%$

Step-by-step solution

Here,

P=\frac{a^3 b^2}{c d}

\begin{aligned} \therefore \frac{\Delta P}{P} & \times 100 = \left(\frac{3 \Delta a}{a}+\frac{2 \Delta b}{b}+\frac{\Delta c}{c}+\frac{\Delta d^{\prime}}{d}\right) \times 100 \\ = & 3 \frac{\Delta a}{a} \times 100+2 \frac{\Delta b}{b} \times 100+\frac{\Delta c}{c} \times 100+\frac{\Delta d^{\prime}}{d} \times 100 \\ = & 3 \times 1+2 \times 2+3+4 \\ = & 3+4+3+4=14 \% \end{aligned}

$$

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